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University of Alberta
Application of continuous wavelet analysis to hyperspectral data for the
characterization of vegetation
by
Tao Cheng
A thesis submitted to the Faculty of Graduate Studies and Research
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy
Department of Earth and Atmospheric Sciences
©Tao Cheng
Fall 2010
Edmonton, Alberta
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis
and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is
converted to, or otherwise made available in digital form, the University of Alberta will advise potential
users of the thesis of these terms.
The author reserves all other publication and other rights in association with the copyright in the thesis and,
except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or
otherwise reproduced in any material form whatsoever without the author's prior written permission.
Examining Committee
Benoit Rivard, Earth and Atmospheric Sciences
rturo nchez-Azofeifa, Earth and Atmospheric Sciences
Arie Croitoru, Earth and Atmospheric Sciences
Herb Yang, Computing Science
Stéphane Jacquemoud, Space and Planetary Geophysics, Université Paris Diderot
ABSTRACT
This thesis explores the application of continuous wavelet analysis (CWA)
to hyperspectral data for the characterization of vegetation at the leaf level. The
first study dealt with the spectral detection of green attack damage (pre-visual
stress) due to mountain pine beetle (Dendroctonus ponderosae Hopkins)
infestation that occurs on lodgepole pines at an early stage, in contrast to
considerable research on the remote detection of red attack damage. A new
methodology was developed to separate healthy pine trees from beetle infested
trees, based on the CWA of hyperspectral measurements for pine needles. This
pilot study showed that a decline in water content occurred for the pine trees at
the green attack stage and the spectral response to that physiological change could
be detected using a few features in the wavelet domain. The second topic
addressed the application of CWA to the determination of leaf water content from
remotely sensed reflectance. Unlike most previous studies involving a limited
number of species, this study examined a wide range of tropical forest species
with the aim to determine reliable and effective wavelet features (coefficients)
sensitive to changes in leaf gravimetric water content (GWC). Of those significant
wavelet features extracted, some related to the absorption of leaf water while
more related to the absorption of dry matter. An evaluation of the wavelet features
as compared with published water indices indicated their great potential for the
estimation of leaf GWC. Lastly, the third study tested the wavelet-based
methodology developed in the second study using a leaf spectral database
generated by the PROSPECT radiative transfer model. The ability of PROSPECT
to simulate leaf reflectance measured for the tropical data set was first assessed.
Then the performance of the aforementioned methodology was evaluated in terms
of the consistency of wavelet features extracted across data sets. This work
demonstrated the effectiveness of the wavelet-based methodology and the
robustness and reliability of recurrent wavelet features for the estimation of leaf
GWC across a wide range of species.
ACKNOWLEDGEMENTS
I am very grateful to my supervisor Dr. Benoit Rivard who provides continuous
support and plenty of critical inputs to the work during the course of my PhD
degree. I also appreciate the insightful discussions through which he inspires my
thinking but never interfere with my decision on what to do next. He always
encourages me to explore my own research interests and helps to keep me on the
right track. I enjoy being a part of his research team that is highly experienced in
hyperspectral data analysis.
I would like to thank Dr. Arturo Sánchez-Azofeifa who inspires me to explore
science problems at University of Alberta and to bring my research into the
context of ecology and environmental science through the interesting group
meetings. I am thankful to him along with Dr. Rivard for having me involved with
the mountain pine beetle project from which I gained experience on field work
and saw how remote sensing could be used to solve a practical problem. He also
supported my research by providing the field datasets used in Chapter Three and
Chapter Four.
Among the professors with CEOS, I am grateful to Dr. Arie Croitoru and Dr. John
Gamon for their useful comments on my candidacy exam. I really enjoyed Dr.
Croitoru’s E 522 course that drove me to get started with programming for
image processing in Matlab. Dr. Gamon encouraged me to learn more about plant
physiology. A few people at the university who generously helped to read through
my thesis and provided useful comments on language editing are Dr. Paula Brook
(Chapter Three), Dr. Patricia Rempel (Chapters One & Five) and Donnette
Thayer (Chapter Three).
Thanks to a few people for their help with the field work. Mei Mei Chong was
very helpful for coordinating several field campaigns and assisting in data
collection in the field. She also trained me to measure chlorophyll in the
laboratory. Dr. Janusz Zwiazek, along with Dr. Monica Calvo-Polanco who co-
authored the paper version of Chapter Two, helped me with designing the girdling
experiment and collecting girdled samples. I am also thankful to Ms. Alena
Prolova for field work assistance and Ms. Nicola Laberge for assistance with field
and laboratory data collection.
I am thankful to Drs. Jilu Feng and Derek Rogge for their discussions about
hyperspectral data processing and IDL coding, especially to Dr. Feng for sharing
the knowledge about wavelet analysis. Ms. Yingduan Huang and her husband
gave me a lot of help with living in Edmonton. I thank this couple for sharing
with me so many overseas living experiences. Thanks to other members in EOSL
for keeping the lab a good academic environment.
Special thanks to my wife, Ms. Qiqi Qu for experiencing the student life with me
and making it so interesting. Her love is great support to my PhD studies. Thank
you to my parents who always encourage me to pursue my interest and to make
decisions on my own. Thank you to my brothers with whom I had so much fun in
the countryside. We are supportive to each other all the time. Thanks should also
be extended to my parents-in-law for their generous support. I cannot imagine
how far I could go on the academic path without the constant support from all
family members.
Lastly, I would like to acknowledge the funding agencies including Alberta
Sustainable Resource Development (Chapter Two), the National Science &
Engineering Research Council of Canada (NSERC) through the Discovery Grant
(Chapter Three), and the National Science Foundation (Chapter Three). Part of
this work (Chapters Three and Four) was funded with the support of the Inter
American Institute for Global Change Research via their Collaborative Network
Program, specifically Tropi-Dry (CRN2-021) via a grant from the U.S. National
Science Foundation (GEO-0452325). The J Gordin Kaplan Graduate Student
Award is acknowledged for supporting the travel to IGARSS 2010 in Honolulu,
Hawaii.
TABLE OF CONTENTS
CHAPTER 1 – INTRODUCTION ......................................................................... 1
1.1. Background .............................................................................................. 1
1.2. Thesis goal and objectives........................................................................ 4
1.3. Thesis outline ........................................................................................... 5
1.4. References ................................................................................................ 7
CHAPTER 2 – CONTINUOUS WAVELET ANALYSIS FOR THE
DETECTION OF GREEN ATTACK DAMAGE DUE TO MOUNTAIN PINE
BEETLE INFESTATION ..................................................................................... 11
2.1. Introduction ............................................................................................ 11
2.2. Data collection........................................................................................ 14
2.2.1. Study sites........................................................................................ 14
2.2.2. Sampling of needles ........................................................................ 15
2.2.3. Measurement of reflectance ............................................................ 16
2.2.4. Measurement of pigment and water content ................................... 16
2.3. Methodology .......................................................................................... 17
2.3.1. Continuous wavelet transform ........................................................ 17
2.3.2. Statistical analysis of leaf pigment and water properties ............... 19
2.3.3. Correlation scalograms .................................................................. 19
2.3.4. Feature selection using correlation scalograms............................. 20
2.4. Results .................................................................................................... 21
2.4.1. Leaf pigment and water properties ................................................. 21
2.4.2. Continuous wavelet analysis of the girdled datasets ...................... 22
2.4.3. Continuous wavelet analysis of the infested datasets ..................... 23
2.5. Discussion .............................................................................................. 24
2.5.1. Regression models for the infested datasets ................................... 24
2.5.2. Selection of scales for scalograms .................................................. 25
2.5.3. Wavelength regions of selected features ......................................... 26
2.5.4. Implications for airborne detection of MPB infestation ................. 26
2.5.5. Potential improvements .................................................................. 28
2.6. Conclusions ............................................................................................ 28
2.7. References .............................................................................................. 30
CHAPTER 3 – SPECTROSCOPIC DETERMINATION OF LEAF WATER
CONTENT USING CONTINUOUS WAVELET ANALYSIS........................... 51
3.1. Introduction ............................................................................................ 51
3.2. Data set ................................................................................................... 53
3.2.1. Site description................................................................................ 53
3.2.2. Data collection ................................................................................ 54
3.3. Methods .................................................................................................. 54
3.3.1. Estimation of leaf gravimetric water content .................................. 54
3.3.2. Wavelet analysis.............................................................................. 55
3.3.3. Continuous wavelet transform (CWT) ............................................ 56
3.3.4. Feature selection from correlation scalograms .............................. 58
3.3.5. Spectral indices ............................................................................... 59
3.3.6. Calibration and validation of regression models ........................... 59
3.4. Results .................................................................................................... 60
3.4.1. Response of leaf reflectance to variations in leaf water content .... 60
3.4.2. Correlation of water indices with leaf water content for a wide
range of species..... ......................................................................... 60
3.4.3. Most informative wavelet features to estimate leaf water content .. 61
3.4.4. Prediction of leaf water content using the wavelet features ........... 62
3.5. Discussion .............................................................................................. 63
3.5.1. Wavelet features for the estimation of leaf water content............... 63
3.5.2. Why do spectral indices not work? ................................................. 64
3.5.3. Advantages of the continuous wavelet analysis .............................. 65
3.5.4. Improvements of leaf water content by dry mass (LWCD) .............. 66
3.6. Conclusion .............................................................................................. 67
3.7. References .............................................................................................. 69
CHAPTER 4 – EVALUATION OF THE PROSPECT MODEL AND
CONTINUOUS WAVELET ANALYSIS FOR EFFICIENT ESTIMATION OF
LEAF WATER CONTENT .................................................................................. 92
4.1. Introduction ............................................................................................ 92
4.2. Materials and methods ........................................................................... 94
4.2.1. Description of leaf reflectance and mass measurements ................ 94
4.2.2. Simulation of leaf reflectance with the PROSPECT model ............ 95
4.2.2.1. Principle of the PROSPECT model….………………………95
4.2.2.2. Parameterization for the simulations…………..…………….95
4.2.3. Feature extraction from wavelet analysis to estimate leaf GWC ... 97
4.2.3.1. Wavelet analysis ……………..................................................97
4.2.3.2. Continuous wavelet transform (CWT)….…….………….......98
4.2.3.3. Feature selection from correlation scalograms …...………...99
4.2.4. Calculation of spectral indices ....................................................... 99
4.3. Results .................................................................................................. 100
4.3.1. Experiment I: simulation of the measured leaf reflectance .......... 100
4.3.2. Experiment II: simulation of leaf spectra for the estimation of leaf
GWC…. ........................................................................................ 101
4.3.2.1. Feature regions determined from the correlation
scalogram……………………………………………..…….101
4.3.2.2. Wavelet features most strongly correlated to LWCF ….……101
4.3.2.3. Relative performance of wavelet features and spectral
indices…..……..……………..……………………………..102
4.3.2.4. Transformation of LWCF to LWCD ………………………...102
4.4. Discussion ............................................................................................ 103
4.4.1. Advantages of the continuous wavelet analysis ............................ 103
4.4.2. Comparison of wavelet features derived from the simulated spectra
and the measured spectra ............................................................. 104
4.4.3. Distribution of spectral information across scales ....................... 105
4.5. Conclusions .......................................................................................... 106
4.6. References ............................................................................................ 108
CHAPTER 5 - CONCLUSIONS ........................................................................ 127
5.1. Summary .............................................................................................. 127
5.2. Synthesis of contributions .................................................................... 127
5.3. Avenues of future research ................................................................... 130
5.4. References ............................................................................................ 134
APPENDIX …………………………………………………………………….137
Appendix 1. Continuous wavelet analysis of a reflectance spectrum ...…137
Appendix 2. Workflow of the wavelet-based methodology .......................139
LIST OF TABLES
Table 2-1. Description of sample size for each dataset ................................................. 37
Table 2-2. Correlation coefficient (r) between chemical properties derived from the
Lodgepole Pine needle samples .................................................................................... 38
Table 2-3. p-values of two-tailed paired student’s t-test results for control and
treatment samples for each dataset ................................................................................ 39
Table 2-4. Properties of features selected from the intersection of correlation
scalograms for the girdled datasets ............................................................................... 40
Table 2-5. Properties of features selected from the intersection of correlation
scalograms for the infested datasets. ............................................................................. 41
Table 2-6. Summary of leaf water content (%) for four datasets with significant
differences between control and treatment samples. ..................................................... 42
Table 3-1. Summary of studies on the spectroscopic determination of leaf water
content with a focus on LWCD and LWCF. The references are indexed by the year of
publication and summarized with the species examined, the spectral range of the
reflectance data, the analytical method, the expression of leaf water content, and the
best result within each study. Note that the studies not related to LWCD and LWCF but
only related to EWT are beyond the scope of this research and not listed. .................. 76
Table 3-2. Summary of water content measurements for 265 leaf samples collected
from tropical forests in Panama. ................................................................................... 78
Table 3-3. Spectral indices for predicting vegetation water content ............................. 79
Table 3-4. Coefficients of determination (R2) for correlations between water content
and spectral metrics (wavelet features and spectral indices) derived from the calibration
set (n = 159) .................................................................................................................. 80
Table 3-5. Wavelet features related to major absorptions of particular leaf biochemical
constituents and obtained for LWCD using the calibration set ...................................... 81
Table 3-6. Coefficient of determination (R2) and RMSE values comparing the
measured water content with that estimated from the predictive models applied to the
validation set (n = 106). ................................................................................................ 82
Table 4-1. Ranges of input variables used for the PROSPECT simulations in
Experiment II .............................................................................................................. 113
Table 4-2. List of wavelet features ranked by R2 using the calibration set and relating
wavelet power to measured leaf water content ........................................................... 114
Table 4-3. Accuracies for the estimation of LWCF in the validation set using spectral
indices, individual wavelet features or a combination of wavelet features derived from
the simulated spectra. .................................................................................................. 115
Table 4-4. Accuracies for the estimation of LWCFin the validation set using individual
wavelet features derived from the measured spectra. ................................................. 116
LIST OF FIGURES
Fig. 2-1. Locations of the study sites in Alberta, Canada. ............................................ 43
Fig. 2-2. Mexican Hat wavelets of scales 5 and 6 draped on a reflectance spectrum of
healthy needles. The wavelet of scale 5 is an approximate match for the wavelength
width of the green peak and the reversed wavelet of scale 6 is a reasonable match for
the width of a major water absorption center. This feature and the green peak would be
captured by wavelets of scale 6 and 5, respectively. ..................................................... 44
Fig. 2-3. Visualization of scalograms: (A) Scale interpolated; (B) Scale replicated.
Scalograms were produced with the Aug14-2008 dataset (water features shown in
blue). Wavelength is displayed along the horizontal direction and scale along the
vertical axis. The R2 value at each wavelength and scale is displayed as amplitude or
brightness. ..................................................................................................................... 45
Fig. 2-4. Example of the frequency distribution of R2 values observed for the
scalogram in Fig. 2-3B. The cut-off R2 value used to delineate features correlated to
biochemical properties or class ID is defined by the highest R2 values encompassing
1% of the data. .............................................................................................................. 46
Fig. 2-5. Structure and labeling of feature sets derived from correlation scalograms
indexed alphabetically from A to U. For example, the feature set A is derived from the
correlation scalogram for the independent variable chlorophyll and the dataset Jun18-
2007; D. A ∩ B refers to feature set D obtained by the intersection of feature set A and
feature set B; E ∩ I = indicates that the intersection of feature set E and feature set I
is an empty set. .............................................................................................................. 47
Fig. 2-6. Correlation scalograms A-K listed in Fig. 2-5 for the girdling datasets. The
selected features are shown in blue on scalograms. ...................................................... 48
Fig. 2-7. Correlation scalograms L-U listed in Fig. 2-5 for the infested datasets. ........ 49
Fig. 2-8. Relationships between water content and the wavelet power at 1320 nm and
scale 7 for the infested datasets: (A) combined control and infested data for July and
August, (B) control and infested for July, (C) control and infested for August. The
thicker solid and dashed lines in (B) and (C) are those seen in (A). ............................. 50
Fig. 3-1. Schematic representation of the feature extraction method using continuous
wavelet analysis. Input data sets include the water content and reflectance
measurements of leaf samples. Output is a list of wavelet features extracted for the
estimation of leaf water content. ................................................................................... 83
Fig. 3-2. Feature regions extracted from the correlation scalograms relating wavelet
power with water content expressed on the basis of (A) dry mass (LWCD) and (B)
fresh mass (LWCF) in the calibration dataset (n = 159). ............................................... 84
Fig. 3-3. Example spectra illustrating the effect of different amounts of LWCD on the
reflectance response. Note the change in the amplitude of reflectance in the 1300–2500
nm region and the variations in depth and shape of the absorption features in the
wavelength regions 1670–1830 nm and 2000–2200 nm (denoted by the horizontal
bars) as LWCD changes from the minimum (32.31%) to the maximum (418.18%)
value. ............................................................................................................................. 85
Fig. 3-4. Relationships between water content and spectral indices calculated from the
calibration set. Rows represent the same spectral indices. The left column is for LWCD
and the right column for LWCF. All relationships are statistically significant (p<0.005).
...................................................................................................................................... 86
Fig. 3-5. Wavelength location of wavelet features indicated by vertical lines and the
corresponding wavelets. The two reflectance spectra are associated with highest (top)
and lowest (bottom) LWCD. Each wavelet feature is positioned on the spectra with the
scaled and shifted continuous wavelet used to compute the wavelet power. The three
numbers beside each vertical line are wavelengths of start, center and end points of the
wavelet. The two dashed vertical lines denote two features which are removed during
the stepwise multiple regression procedure. ................................................................. 87
Fig. 3-6. Relationships between the wavelet power at (2165 nm, 4) and water content
(A) LWCD and (B) LWCF established with the calibration data set (p<0.0001). The
solid lines are for the entire data set and the dashed line in (A) is for a subset excluding
observations of LWCD above 250%.............................................................................. 88
Fig. 3-7. (A) and (B) are plots of measured versus predicted water contents LWCD
using wavelet feature (2165, 4) and a combination of six features (I, Table 3-6),
respectively. (C) and (D) are plots of measured versus predicted LWCF using wavelet
feature (2165 nm, 4) and a combination of six features, respectively. The predictive R2
and RMSE values shown are obtained for the validation set. Dashed lines are 1:1 lines.
...................................................................................................................................... 89
Fig. 3-8. Inter-relationships between wavelet power, LWCD, and LWCF. ................... 90
Fig. 3-9. Measured versus predicted LWCD transformed from LWCF estimates
presented in Fig. 3-7 C and D. Note the differences as compared to the upper plots in
Fig. 3-7. ......................................................................................................................... 91
Fig. 4-1. Histograms of leaf water content by fresh weight (LWCF) derived from (A)
the laboratory measurements on each leaf and (B) values of Cw and Cm for the
PROSPECT simulations. ............................................................................................ 117
Fig. 4-2. (A) Plot of mean and mean ± s.d. of reflectance spectra for the measured leaf
reflectance dataset and the PROSPECT simulated dataset. (B) The root mean square
error (RMSE) per wavelength as described in Eq. (4-1). The dashed circles highlight
spectral regions displaying local minimum in RMSE. ................................................ 118
Fig. 4-3. Features regions extracted from the correlation scalogram relating wavelet
power and leaf water content (LWCF). The feature with strongest correlation (1740 nm,
4) originates from the largest feature region. Arrows mark the wavelength position of
wavelet features representative of each feature region. .............................................. 119
Fig. 4-4. Wavelet features used for the estimation of LWCF. The wavelength position
and scale of those features are indicated by vertical lines and the corresponding
wavelets. Also shown are reflectance spectra for highest LWCF (dashed line) and
lowest LWCF (dotted line). Each wavelet feature is positioned on the spectra with the
scaled and shifted continuous wavelet used to compute its wavelet power. (A) Wavelet
features derived from the PROSPECT simulated reflectance spectra. (B) Wavelet
features derived from the measured reflectance spectra. ............................................ 120
Fig. 4-5. (A) Correlation between the best performing wavelet feature (1740 nm, 4)
and leaf water content (LWCF) for the calibration set. (B) Estimates of LWCF derived
from the regression model in (A). ............................................................................... 121
Fig. 4-6. Plot of actual versus predicted LWCF derived using a combination of the six
wavelet features for the simulated spectra. ................................................................. 122
Fig. 4-7. (A) Relationship between the water index (WI) and leaf water content
(LWCF) for the calibration set. (B) Estimates of LWCF derived with the regression
model in (A). ............................................................................................................... 123
Fig. 4-8. Actual LWCD plotted against predicted LWCD inverted from LWCF
estimates. The LWCF were obtained from wavelet feature (1740 nm, 4) for (A) and
from the combination of all features for (B). .............................................................. 124
Fig. 4-9. Effects of leaf properties on the reflectance simulated by the PROSPECT
model: (A) leaf structure, (B) equivalent water thickness, and (C) dry matter content.
Also shown in (D) is the coupled effect of equivalent water thickness and dry matter
content. ........................................................................................................................ 125
Fig. 4-10. Example PROSPECT-simulated reflectance spectra with randomly
generated combinations of LWCF and N. Note that reflectance spectra simulated with
higher LWCF values should display lower reflectance in the infrared region but do not
as a result of unrealistic combinations of input variables. .......................................... 126
Fig. A-1. Schematic representation of the continuous wavelet transform workflow..137
Fig. A-2. Workflow of the wavelet-based methodology.............................................139
LIST OF SYMBOLS AND ABBREVIATIONS
AIC kaike’s information criterion
Ca+b Leaf chlorophyll a+b concentration
Cm Leaf dry matter content
Cw Leaf equivalent water thickness
CWA Continuous wavelet analysis
CWT Continuous wavelet transform
DMC Dry matter content
DMSO Dimethyl sulphoxide
DOG Derivative of Gaussian
DW Dry weight
DWT Discrete wavelet transform
EWT Equivalent water thickness
FS Fort Sherman
FW Fresh weight
GA-PLS Genetic algorithms partial least squares
GWC Gravimetric water content
LAI Leaf area index
LOPEX Leaf optical properties experiment
LWCD Leaf water content as percent of dry mass
LWCF Leaf water content as percent of fresh mass
MPB Mountain pine beetle
MSI Moisture stress index
N Leaf structure parameter
NDWI Normalized difference water index
NIR Near infrared
PLS Partial least squares
PNM Parque Natural Metropolitano
PROSPECT A model of leaf optical properties spectra
RMSE Root mean square error
RWC Relative water content
SMLR Stepwise multiple linear regression
STRI Smithsonian Tropical Research Institute
SWIR Shortwave infrared
VIS Visible
WI Water index
1
CHAPTER 1 – INTRODUCTION
1.1. Background
As a key component of the earth system, vegetation influences the energy
and mass exchange with the atmosphere and soil, particularly the cycling of
carbon, water and nutrient in terrestrial ecosystems. Remote sensing, precisely
imaging spectroscopy, offers an effective way to detect the spatial variations in
chemical constituents of vegetation canopies such as pigment, water, nitrogen and
carbon constituents at broad spatial scales and their relations with biodiversity and
the Earth’s climate system (Asner & Vitousek, 2005; Ollinger et al., 2008; Ustin
et al., 2004). Over the last few decades, imaging spectrometer data acquired from
aircraft or spacecraft have become increasingly available for developing remote
sensing techniques to estimate canopy chemistry in various forest ecosystems.
(Coops et al., 2003; Martin & Aber, 1997; Peterson et al., 1988; Townsend et al.,
2003; Wessman et al., 1988). Following these successful estimations at the
landscape level, the spatial distribution of ecosystem chemical composition over
large portions of the globe may be revealed in the near future by a few new
hyperspectral satellite missions such as HyspIRI and EnMAP (Kokaly et al.,
2009).
Compared to imaging spectrometers that remotely measure the reflectance
of plant canopies in hundreds of narrow and contiguous spectral bands (Goetz et
al., 1985), laboratory spectrometers are able to measure the reflectance of leaves
in thousands of spectral bands in a laboratory setting. The reflectance
measurements from the former are more complex than those from the latter due to
the impact of such factors as canopy structural variation and viewing geometry
(Clark et al., 2005; Roberts et al., 2004). Therefore, the application of imaging
spectroscopy to plant canopies could benefit from the advancement of laboratory
research in which leaf chemical properties are more accurately estimated from
higher quality spectroscopic data measured in more controlled conditions.
2
Previous laboratory studies on the determination of leaf chemistry have
contributed significantly to our understanding of leaf spectral responses
associated with changes in chemical concentrations (Asner & Martin, 2008;
Curran, 1989; Curran et al., 2001; Kokaly, 2001; Kokaly & Clark, 1999). In
addition, quantitative chemical information derived from leaf reflectance is of
importance for the detection of vegetation stresses caused by the insufficient
availability of such foliar chemicals as water, nitrogen, and total chlorophyll in
plant physiological processes (Pu et al., 2008; Strachan et al., 2002; Zarco-Tejada
et al., 2002).
The reflectance spectra for different types of vegetation (400-2500 nm) are
similar in shape because vegetation reflectance is mainly influenced by the
spectral absorptions of common chemical components weighted by their
concentrations (Curran, 1989; Kokaly & Clark, 1999). Due to the spectral
absorptions by multiple chemicals, it is difficult to uniquely relate the reflectance
at a wavelength to the concentration of a single chemical constituent in leaves.
One solution to that problem is to utilize more than one wavelength to enhance
the absorption features being examined and suppress the spectral variability
caused by factors irrelevant to leaf chemistry (e.g., illumination variation).
In order to resolve the absorption of a leaf chemical constituent with
multiple wavelengths, many studies use stepwise multiple linear regression
(SMLR) to build calibration equations by selecting a small number of
wavelengths that separately correlate with concentrations of each of such
constituents as water, nitrogen, lignin, cellulose (Card et al., 1988; Curran et al.,
1992; Gross et al., 1996). Two spectral preprocessing techniques have often been
applied prior to the regression: derivative analysis and continuum removal.
Derivative analysis, performed by means of applying the first or second derivative
to reflectance spectra, has been widely used to emphasize subtle absorption
features of leaf chemicals due to its lower sensitivity to illumination intensity and
leaf internal structural variability (Curran et al., 1992; Danson et al., 1992;
Johnson & Billow, 1996; Pe uelas et al., 1994). This approach does not provide a
3
flexible way to extract meaningful information on absorption features of various
widths at a time (Bruce & Li, 2001). In addition, the sensitivity of derivative
spectra to noise in reflectance spectra poses a problem for the effectiveness of
second- or higher-order derivatives. Continuum removal is a spectral analysis tool
specifically designed to isolate absorption features of interest from the continuum
of reflectance spectra. The use of continuum-removed spectra enables us to build
direct relationships between concentrations of chemical constituents and
absorption characteristics (Curran et al., 2001; Kokaly, 2001; Kokaly & Clark,
1999). However, the shape of continuum-removed spectra is non-deterministic
because it is subject to the analyst’s definition of the absorption region of interest
and to the choice of an algorithm to approximate the continuum (Rivard et al.,
2008).
To avoid the direct use of reflectance or derivative reflectance, one can
use spectral indices that are band ratios of spectral reflectance at a small number
of wavelengths. However, spectral indices are often empirically developed
through correlation between chemical concentrations and leaf spectral properties
for a few species that are close in geographic location or taxonomy (Blackburn,
1998; Eitel et al., 2006; Pe uelas et al., 1997). Those empirical relationships tend
to become weaker when spectral indices are applied to a data set that exhibits
much diversity in species composition and substantial variation in leaf spectral
properties. Thus, further investigations are required to develop more robust
relationships to reduce the spectral variation irrespective of leaf chemical
properties by incorporating more informative wavelengths (Datt, 1999a; Datt,
1999b; le Maire et al., 2004; Sims & Gamon, 2002). Recently, continuous wavelet
analysis (CWA) has emerged as a promising tool in laboratory spectroscopy for
deriving chemical properties from leaf reflectance spectra (Blackburn &
Ferwerda, 2008; Ferwerda & Jones, 2006). CWA enables us to decompose a
reflectance spectrum into a number of scale components each of which is directly
comparable to a reflectance spectrum and therefore readily linked to the
absorption features. The multi-scale representation of a reflectance spectrum
facilitates the characterization of absorption features of different widths at various
4
scales. These characteristics of CWA offer a valuable opportunity to gain new
insights into the spectral responses associated with changes in leaf chemical
constituents.
1.2. Thesis goal and objectives
The main goal of this thesis is to investigate the application of CWA to the
characterization of vegetation using hyperspectral data. The objectives are: 1) to
develop methodologies based on continuous wavelet analysis of reflectance
spectra for two specific applications: the early detection of beetle attack damage
and the estimation of leaf water content across a variety of tropical species, and 2)
to evaluate the generality of the methodology developed for the estimation of leaf
water content using a modeling approach. Specifically, the first objective
addresses how to use spectral signatures of pine needles to detect the insufficiency
of water and chlorophyll as a physiological response to beetle infestation, and
what spectral features are the most sensitive to changes in leaf water content. The
second objective addresses the use of a simulated data set generated by a leaf
radiative transfer model (PROSPECT) to test the wavelet-based methodology
developed using a laboratory-measured data set. This research focuses on
understanding the fundamentals of leaf-level spectral variations in relation to
changes in concentrations of leaf water and chlorophyll through the use of CWA.
It is therefore expected to be extended to canopy or landscape level in the future.
Those methodologies, although specifically developed for the early detection of
beetle attack damage and estimation of leaf water content in this thesis, should
also assist in the stress detection and in the retrieval of any leaf biochemical
constituent in other vegetation studies that use reflectance spectroscopy as a main
tool.
5
1.3. Thesis outline
This thesis is based on the compilation of three standalone papers
published or submitted to peer-reviewed journals. Following the introduction, the
three chapters deal with the application of continuous wavelet analysis to
reflectance spectra coupled with leaf trait data (total chlorophyll and water) for
characterizing vegetation conditions.
The main goal of Chapter 2 is to search for spectral signals that relate to
the early detection of the effect of mountain pine beetle (Dendroctonus
ponderosae Hopkins) infestation on the spectral response of lodgepole pines. To
detect the pre-visual beetle attack damage, two research questions were
addressed: 1) do infested trees undergo water stress, chlorophyll stress, or both?
2) if any of these stresses occurs, is the stress detectable using spectral
reflectance? Several field campaigns were conducted to collect measurements of
needle spectral reflectance, total chlorophyll concentration, and water content
from healthy pine trees and infested trees that were at the green attack stage.
Statistical analysis was performed on chlorophyll and water data to achieve a
good understanding of the physiological mechanism of the green attack damage
and provide guidance for subsequent spectral analysis. To detect the potential
stress in the spectral domain, a novel method was developed to spectrally
distinguish healthy trees from infested trees using CWA of reflectance spectra.
This study, Continuous wavelet analysis for the detection of green attack damage due to
mountain pine beetle infestation (Cheng et al., 2010), was published in Remote
Sensing of Environment, 114, 899-910.
As Chapter 2 concludes that the water content of needles is a physiological
indicator of the green attack damage, Chapter 3 focuses on determining the most
reliable spectral information that relates to the water content in a leaf.
Measurements of leaf reflectance and gravimetric water content (GWC) for 47
tropical forest species in Panama were collected from 265 leaf samples to
represent the wide ranges of water content and spectral variability (Castro et al.,
2006; Sánchez-Azofeifa et al., 2009). Using CWA, an effective method was
developed to determine the most significant wavelet features that are sensitive to
6
changes in leaf GWC across a variety of species. The performance of the wavelet
features extracted using this new method was evaluated and compared with that of
common spectral indices for the estimation of leaf GWC. In addition, the
significance of those wavelet features was interpreted with reference to absorption
features in leaf reflectance spectra.
In Chapter 4, I test the wavelet-based methodology developed in Chapter 3
using the leaf reflectance spectra simulated by the PROSPECT radiative transfer
model. Input parameters for simulations with PROSPECT were defined based on
the measurements of the tropical leaf data set used in Chapter 3. Two experiments
were conducted, each with different simulation conditions. One was designed for
assessing the ability of PROSPECT to simulate the measured reflectance in the
tropical leaf data set. The other was used to evaluate the performance of the
wavelet-based methodology for the estimation of leaf GWC from simulated
spectra. The wavelet features derived from the simulated spectra were compared
with common water indices in terms of the predictive capabilities. More
importantly, these wavelet features were compared to those from the measured
spectra to determine the robust wavelet features sensitive to changes in leaf GWC
across data sets. This research in conjunction with the study in Chapter 3 provides
a new insight into explaining the spectral variations caused by changes in leaf
GWC through the use of CWA.
Lastly, I close this thesis by summarizing the conclusions presented in the
three chapters above and describing the directions of future research.
7
1.4. References
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forests: Scaling from leaf to canopy levels. Remote Sensing of
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and biogeochemical change. Proceedings of the National Academy of
Sciences of the United States of America, 102, 4383-4386.
Blackburn, G. A. (1998). Spectral indices for estimating photosynthetic pigment
concentrations: A test using senescent tree leaves. International Journal of
Remote Sensing, 19, 657-675.
Blackburn, G. A., & Ferwerda, J. G. (2008). Retrieval of chlorophyll
concentration from leaf reflectance spectra using wavelet analysis. Remote
Sensing of Environment, 112, 1614-1632.
Bruce, L. M., & Li, J. (2001). Wavelets for computationally efficient
hyperspectral derivative analysis. IEEE Transactions on Geoscience and
Remote Sensing, 39, 1540-1546.
Card, D. H., Peterson, D. L., Matson, P. A., & Aber, J. D. (1988). Prediction of
leaf chemistry by the use of visible and near infrared reflectance
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Cheng, T., Rivard, B., Sánchez-Azofeifa, G. A., Feng, J. & Calvo-Polanco, M.
(2010). Continuous wavelet analysis for the detection of green attack damage
due to mountain pine beetle infestation. Remote Sensing of Environment,
114, 899-910.
Clark, M. L., Roberts, D. A., & Clark, D. B. (2005). Hyperspectral discrimination
of tropical rain forest tree species at leaf to crown scales. Remote Sensing of
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of eucalypt foliage nitrogen content from satellite-derived hyperspectral
data. IEEE Transactions on Geoscience and Remote Sensing, 41, 1338-1346.
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(1992). Reflectance spectroscopy of fresh whole leaves for the estimation of
chemical concentration. Remote Sensing of Environment, 39, 153-166.
8
Curran, P. J., Dungan, J. L., & Peterson, D. L. (2001). Estimating the foliar
biochemical concentration of leaves with reflectance spectrometry: Testing
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349-359.
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resolution data for determining leaf water content. International Journal of
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Eitel, J. U. H., Gessler, P. E., Smith, A. M. S., & Robberecht, R. (2006).
Suitability of existing and novel spectral indices to remotely detect water
stress in populus spp. Forest Ecology and Management, 229, 170-182.
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Grossman, Y. L., Ustin, S. L., Jacquemoud, S., Sanderson, E. W., Schmuck, G., &
Verdebout, J. (1996). Critique of stepwise multiple linear regression for the
extraction of leaf biochemistry information from leaf reflectance data.
Remote Sensing of Environment, 56, 182-193.
Johnson, L. F., & Billow, C. R. (1996). Spectrometric estimation of total nitrogen
concentration in douglas-fir foliage. International Journal of Remote
Sensing, 17, 489-500.
Kokaly, R. F. (2001). Investigating a physical basis for spectroscopic estimates of
leaf nitrogen concentration. Remote Sensing of Environment, 75, 153-161.
Kokaly, R. F., Asner, G. P., Ollinger, S. V., Martin, M. E., & Wessman, C. A.
(2009). Characterizing canopy biochemistry from imaging spectroscopy and
its application to ecosystem studies. Remote Sensing of Environment, 113,
S78-S91.
9
Kokaly, R. F., & Clark, R. N. (1999). Spectroscopic determination of leaf
biochemistry using band-depth analysis of absorption features and stepwise
multiple linear regression. Remote Sensing of Environment, 67, 267-287.
le Maire, G., François, C., & Dufrêne, E. (2004). Towards universal broad leaf
chlorophyll indices using PROSPECT simulated database and hyperspectral
reflectance measurements. Remote Sensing of Environment, 89, 1-28.
Martin, M. E., & Aber, J. D. (1997). High spectral resolution remote sensing of
forest canopy lignin, nitrogen, and ecosystem processes. Ecological
Applications, 431-443.
Ollinger, S. V., Richardson, A. D., Martin, M. E., Hollinger, D. Y., Frolking, S.
E., Reich, P. B., Plorde, L. C., Katul, G. G., Munger, J. W., Oren, R., Smith,
M. –L., Paw U, K. T., Bolstad, P. V., Cook, B. D., Day, M. C., Martin, T. A.,
Monson, R. K. & Schmid, H. P. (2008). Canopy nitrogen, carbon
assimilation, and albedo in temperate and boreal forests: Functional relations
and potential climate feedbacks. Proceedings of the National Academy of
Sciences of the United States of America, 105, 19336-19341.
Penuelas, J., Gamon, J. A., Fredeen, A. L., Merino, J., & Field, C. B. (1994).
Reflectance indices associated with physiological changes in nitrogen- and
water-limited sunflower leaves. Remote Sensing of Environment, 48, 135-
146.
Pe uelas J. Pi ol, J., Ogaya, R., & Filella, I. (1997). Estimation of plant water
concentration by the reflectance water index WI (R900/R970). International
Journal of Remote Sensing, 18, 2869-2875.
Peterson, D. L., Aber, J. D., Matson, P. A., Card, D. H., Swanberg, N., Wessman,
C., Spanner, M. (1988). Remote sensing of forest canopy and leaf
biochemical contents. Remote Sensing of Environment, 24, 85-108.
Pu, R., Kelly, M., Chen, Q., & Gong, P. (2008). Spectroscopic determination of
health levels of coast live oak (Quercus agrifolia) leaves. Geocarto
International, 23, 3-20.
Rivard, B., Feng, J., Gallie, A., & Sánchez-Azofeifa, A. (2008). Continuous
wavelets for the improved use of spectral libraries and hyperspectral data.
Remote Sensing of Environment, 112, 2850-2862.
Roberts, D. A., Ustin, S. L., Ogunjemiyo, S., Greenberg, J., Bobrowski, S. Z.,
Chen, J., & Hinckley, T. M. (2004). Spectral and structural measures of
northwest forest vegetation at leaf to landscape scales. Ecosystems, 7, 545-
562.
10
Sims, D. A., & Gamon, J. A. (2002). Relationships between leaf pigment content
and spectral reflectance across a wide range of species, leaf structures and
developmental stages. Remote Sensing of Environment, 81, 337-354.
Smith, M. L., Ollinger, S. V., Martin, M. E., Aber, J. D., Hallett, R. A., &
Goodale, C. L. (2002). Direct estimation of aboveground forest productivity
through hyperspectral remote sensing of canopy nitrogen. Ecological
Applications, 12, 1286-1302.
Strachan, I. B., Pattey, E., & Boisvert, J. B. (2002). Impact of nitrogen and
environmental conditions on corn as detected by hyperspectral reflectance.
Remote Sensing of Environment, 80, 213-224.
Townsend, P. A., Foster, J. R., Chastain Jr., R. A., & Currie, W. S. (2003).
Application of imaging spectroscopy to mapping canopy nitrogen in the
forest of the central Appalachian mountains using hyperion and
AVIRIS. IEEE Transactions on Geoscience and Remote Sensing, 41, 1347-
1354.
Ustin, S. L., Roberts, D. A., Gamon, J. A., Asner, G. P., & Green, R. O. (2004).
Using imaging spectroscopy to study ecosystem processes and properties.
Bioscience, 54, 523-534.
Vogelmann, J. E., Rock, B. N., & Moss, D. M. (1993). Red edge spectral
measurements from sugar maple leaves. International Journal of Remote
Sensing, 14, 1563-1575.
Wessman, C. A., Aber, J. D., Peterson, D. L., & Melillo, J. M. (1988). Remote
sensing of canopy chemistry and nitrogen cycling in temperate forest
ecosystems. Nature, 335, 154-156.
Zarco-Tejada, P. J., Miller, J. R., Mohammed, G. H., Noland, T. L., & Sampson,
P. H. (2002). Vegetation stress detection through chlorophyll a + b estimation
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Quality, 31, 1433-1441.
11
CHAPTER 2 – CONTINUOUS WAVELET ANALYSIS FOR
THE DETECTION OF GREEN ATTACK DAMAGE DUE TO
MOUNTAIN PINE BEETLE INFESTATION1
2.1. Introduction
The mountain pine beetle (Dendroctonus ponderosae Hopkins) is a native
insect of the pine forests of western Northern America, and significant outbreaks
of its population periodically occur in these stands (Safranyik et al., 1974; Taylor
et al., 2006). In Canada, the beetle population at epidemic levels has been
primarily recorded in British Columbia where the cumulative area of beetle
outbreak was 130,000 km2 by the end of 2006 (Westfall, 2007). However, forest
monitoring indicated an increasing presence of mountain pine beetle and a spread
from west-central Alberta to southwestern and northwestern Alberta since 1992,
consistent with the expansion of mountain pine beetle outbreak areas in British
Columbia (Alberta Sustainable Resource Development, 2007). During great
outbreaks, beetle populations are capable to cause mortality of mature trees over
many thousands of hectares (Safranyik & Carroll, 2006). The beetle-killed trees
have an environmental impact by reducing forest carbon uptake and increasing
future emissions (Kurz et al. 2008)) but they also represent a large economic loss
to the forest industry. Recent research demonstrated that the current outbreak of
mountain pine beetle in western Canada even affected forest carbon dynamics
over large areas and contributed significantly to global climate change (Kurz et
al., 2008).
1 A version of this paper has been published: Cheng, T., Rivard, B., Sánchez-Azofeifa, G.
A., Feng, J. & Calvo-Polanco, M. (2010). Continuous wavelet analysis for the detection
of green attack damage due to mountain pine beetle infestation. Remote Sensing of
Environment, 114, 899-910. Reprinted with permission from Elsevier.
Author contributions: Dr. Rivard and Dr. Sánchez-Azofeifa helped design the whole
study, discussed the results, and provided editing comments on the manuscript. Dr. Feng
was partly involved with discussion about data processing using continuous wavelet
analysis. Dr. Calvo-Polanco helped with site selection and data collection for the girdling
experiment. I collected spectral measurements in the field, did water content and
chlorophyll concentration measurements in the laboratory, wrote the codes for data
processing, processed the data, interpreted the results, and composed the manuscript.
12
The principal hosts killed by mountain pine beetle in western Canada are
mature pine trees of which the lodgepole pine (Pinus contorta Dougl. Ex Loud.
Var latifolia Engelm.) is extensively studied (Safranyik & Carroll, 2006). The
beetle usually starts attacking the healthy trees by colonizing the hosts during late
July through mid August. The trees bear green foliage during the early stage of
attack also referred to as green attack. Subsequently, the damage is transitioned to
red attack with the crown fading to uniform yellow to red and to brown by late
summer of the following year (Amman, 1982; Henigman et al., 1999).
To meet the information needs of the extent and damage level of the
mountain pine beetle infestation, remotely sensed data have been extensively
utilized over large areas (Wulder et al., 2006). In particular, a number of
successful studies have focused on the detection of red attack damage using
multispectral satellite imagery at a range of spatial resolutions (Coops et al.,
2006a; Coops et al., 2006b; Franklin et al., 2003; Skakun et al., 2003; White et al.,
2005; White et al., 2006). Franklin et al. (2003) used stratified Landsat TM
imagery to identify red-attack stands from non-attack forest stands with an overall
classification accuracy of 73%. White et al (2005) used IKONOS imagery to
detect red attack at sites with different intensities of infestation. They obtained
accuracies of 71% and 92% for stands that respectively contained 1-5% and 5-
20% trees with red attack. Using QuickBird imagery, Coops et al (2006a)
generated a ratio of red to green reflectance to distinguish red-attack and non-
attacked pixels and found a significant relationship between the number of red
attack pixels and red attacked crowns observed in the field (r2=0.48, p<0.001,
standard error=2.8 crowns). In this case the identification of red-attack crowns is
viable because the spatial resolution of Ikonos (4m) and QuickBird (2.5m)
multispectral imagery are consistent with the size of individual tree crowns. The
spectral resolution of these data is however insufficient to capture the spectral
response of trees to the biophysical phenomena (e.g., water stress) caused by
beetle attack. White et al (2007) recently examined six moisture indices derived
from EO-1 Hyperion hyperspectral imagery and established a significant
relationship between the Moisture Stress Index and levels of red attack (r2=0.51,
13
p=0.0001). Their study suggests that hyperspectral data may provide a means to
detect the signals from red attacked stands with low densities of infestation.
Studies investigating the spectral detection of green attack are sparse in
the literature. Using foliage reflectance data acquired from 360-1050 nm, Ahern
(1988) determined that the most promising spectral bands for the detection of
green attack were located near the green peak, red edge and near-infrared
shoulder. A red-shift of the red edge position was also observed in the spectra of
trees under green attack. Runesson (1991) investigated the detection of green
attack based on in-situ spectroscopy and digital airborne data and found that the
separation between healthy and attacked tree canopies was poor. In contrast to the
previous study, the analysis of foliage reflectance spectra demonstrated a blue-
shift of the red edge for attacked trees.
The studies by Ahern (1988) and Runesson (1991) paid particular
attention to the examination of pigment-driven spectral variations in the visible
and near infrared regions. Changes in leaf water content and ensuing changes in
leaf spectral reflectance were not investigated or were undetected because spectral
data beyond 1100nm were unavailable. Declines in sapwood moisture content
resulting from beetle attack have been documented (Reid, 1961; Yamaoka et al.,
1990) and consequently moisture stress may result in non-visual symptoms that
are detectable with spectral data particularly if data are acquired between 1000-
2500 nm where water absorption features in vegetation are well documented.
This study examines the spectral properties (350-2500 nm) and total
chlorophyll and water content characteristics of needles obtained from infested
and control (healthy) lodgepole pine trees to assess the detection of pre-visual
symptoms. As a baseline, I also examine these properties for healthy trees and
trees girdled to induce a water stress. The literature provides a number of spectral
indices for the detection of pigment and water variability in leaves (Blackburn,
1998; Gamon et al., 1992; Gao, 1996; Hunt & Rock, 1989; Peñuelas et al., 1993,
1997; Rock et al., 1986; Sims & Gamon, 2002) but these employ only a limited
number of spectral bands. Alternatively wavelet analysis has shown promise for
the analysis of hyperspectral data (Blackburn, 2007; Blackburn & Ferwerda,
14
2008; Ferwerda & Jones, 2006; Kalacska et al., 2007; Koger et al., 2003; Pu &
Gong, 2004; Rivard et al. 2008; Zhang et al., 2006). Wavelet analysis has the
merit of decomposing the reflectance spectra into components of different scales
(or frequencies) thus facilitating the detection of subtle signals. The aim of this
study was to focus on the detection of green attack induced by mountain pine
beetle utilizing leaf-level reflectance spectra analysed with a continuous wavelet
transform. Specifically the study compared the responses of healthy control trees
to infested and girdled trees and investigated the feasibility of separating these
two groups using an appropriate set of spectral features (at particular scales and
wavelength positions).
2.2. Data collection
2.2.1. Study sites
To assess the spectral detection of green attack for pine needles, two sites
located northwest of Edmonton, Alberta, Canada were investigated (Fig. 2-1). The
first site, located near Swan Hills, served for the girdling experiment to simulate
the injury of sapwood tissues by a beetle attack. The second site, located near
Grande Prairie, consisted of trees that were infested by mountain pine beetle
(MPB).
Lodgepole pine (Pinus contorta Dougl. ex Loud. var. latifolia Engelm.)
dominates the forests at the two sites. The trees investigated were approximately
20 years old, 8 meter tall, and displaying a diameter at breast height of 15 cm. At
each site a number of control and treatment pine tree pairs were sampled. The
sites with girdled trees and MPB infested trees encompass 16 and 15 tree pairs,
respectively. Trees showing pitch tubes and bearing green foliage at the beginning
of the sampling period were chosen to comprise the infested samples. The
selected lodgepole pine trees received extensive sunlight occurring along
clearings. Each healthy tree used as control was located within 5 meters of the
treatment tree to facilitate comparison between control and treatment samples.
15
The girdling treatment was implemented in May 2007 to simulate the
effect of MPB infestation where fungus transmitted by the beetle infects the
sapwood and plugs the water-conducting xylem elements (tracheids) effectively
preventing them from conducting water (Solheim, 1995; Yamaoka et al., 1990).
An incision with a saw was made around the trunk of the tree approximately 50
cm above the ground and 5 cm into the sapwood. In doing so I aimed to interrupt
the continuity of xylem tracheids in the tree and interrupt the flow of xylem sap
into the crown. This treatment has been previously used to induce water-deficit
stress in trees (Brix & Mitchell, 1985; Kent et al., 2004; Riggs & Running, 1991;
Running, 1980). All treatment and control pairs at the girdling site were densely
distributed along two roads at two subset sites two kilometers apart. Field
measurements were acquired at this site on June 18th
and August 30th
of 2007.
Infested trees at the second site were attacked by mountain pine beetle in
the summer of 2007 and all tree pairs occurred within an area of 1.5 km2 along a
main road. Field measurements were acquired in 2008 on June 5th
, July 13th
,
August 14th
, September 20th
and October 14th
. All tree samples were bearing
green needles on June 5th
and two trees showing discoloration of foliage on
subsequent dates were excluded from sampling. The final number of trees
available for analysis at each date is shown in Table 2-1.
2.2.2. Sampling of needles
A pole pruner was used in the early afternoon to collect one sunlit branch
from each tree. Needles were then collected throughout the branch excluding new
shoots. Reflectance spectra were either immediately acquired or the branch
samples were packed with ice bags and transported to a nearby indoor laboratory
where they were measured. Within minutes of each spectral measurement,
approximately one third of the needles were wrapped in moistened paper towels
and sealed with foil paper in a cooler with ice (Foley et al., 2006). The samples
were then kept at -18oC for subsequent leaf biochemical analysis.
16
2.2.3. Measurement of reflectance
An optically thick layer of needles extracted from a given branch was
arranged on a panel coated with spectrally flat black paint (maximum reflectance
of 9.8% at 400 nm). The FieldSpec® FR spectroradiometer (ASD Inc., Boulder,
CO, USA) was then used to measure the reflectance of needle samples from 350
to 2500 nm. The instrument is characterized by a resolution of 3 nm at 700 nm, 10
nm at 1500 nm, and 10 nm at 2100 nm. The FieldSpec® FR fiberoptic cable
utilized to collect light reflected from a sample was coupled to a high intensity
reflectance probe attachment which is equipped with an internal artificial light
source thus providing measurements independent of solar illumination conditions.
The probe attachment was placed on the optically thick layer of needles and it
encompassed an approximate field of view of 2.5cm in diameter. The probe was
in contact with the needle layer and excluded external light. Reflectance was
determined by standardizing one sample spectrum to that of a white Spectralon
reference panel (99% reflectance). Each measurement (e.g. sample and reference)
were recorded as an average of twenty scans in order to minimize instrument
noise.
2.2.4. Measurement of pigment and water content
For each sample, two bundles of two needles were placed in a 15 ml
centrifuge tube and pigments were extracted by adding 10 ml of dimethyl
sulphoxide (DMSO) to the tube and placing the tube in a 65°C water bath in the
dark for more than 5 hours. The extract was transferred to a 4.5 ml cuvette and the
absorbance at 664 nm, 646 nm and 470 nm was measured with a Smart® Spectro
spectrophotometer (LaMotte, Chestertown, MD, USA). A blank sample was
measured for calibration once for each wavelength. The concentrations of
chlorophyll a, chlorophyll b and total carotenoids in µg/g were determined using
the coefficients and equations derived by Wellburn (1994).
The remaining needles for each sample were weighted to determine fresh
weight (FW). Dry weight (DW) was then determined by weighing after oven
17
drying at 80°C for 24 hours. The water content of the needles as a percent of dry
mass was given by:
H2O% = ((FW-DW) / DW)×100 (2-1)
2.3. Methodology
2.3.1. Continuous wavelet transform
Wavelet analysis is a powerful signal processing tool (Mallat, 1999) which
has been used successfully in medical sciences (Addison, 2005), geophysics
(Farge, 1992; Torrence & Compo, 1998) and remote sensing image processing
(Núñez et al., 1999; Simhadri et al., 1998) to extract information from various
scales. Past studies include spectral smoothing and noise removal (Schmidt &
Skidmore, 2004), discrimination of weeds from crop (Koger et al., 2003), tree
stress detection (Kempeneers et al., 2005), tropical tree species identification
(Zhang et al., 2006), forest leaf area index (LAI) and crown closure mapping (Pu
& Gong, 2004), and retrieval of foliar pigment content (Blackburn, 2007;
Blackburn & Ferwerda, 2008).
Recent studies (Bruce & Li, 2001; Bruce et al., 2001, 2002, 2006; Li &
Bruce, 2004) have demonstrated the merits of using wavelet deconvolution for the
analysis of hyperspectral data because such data exhibit non-stationarity, that is,
spectral signals can vary in both amplitude (e.g. feature depth) and scale (e.g.
feature width). Wavelet analysis can be implemented as a continuous wavelet
transform (CWT) or a discrete wavelet transform (DWT). Most of the studies
listed above exploited the DWT as a method for feature reduction but a
substantial drawback is the inherent difficulty in interpreting the output
coefficients. The CWT can decompose a signal at a continuum of positions rather
than at dyadic positions and thus the outputs from the CWT are directly
comparable to the original spectrum and are more easily interpretable. Recently,
Rivard et al. (2008) provided an examination of CWT to highlight key spectral
features in mineral spectra. Therefore, CWT was used in this study to examine its
18
potential to extract spectral information of various scales for leaf reflectance
spectra.
The wavelet transform uses a mother wavelet basis function to convert a
hyperspectral reflectance spectrum f(λ) (λ=1, 2,..., n, n is the number of
wavebands and n=2151 herein) into sets of coefficients. The wavelets ψa,b(λ) are
produced by scaling (dilating) and shifting (translating) the mother wavelet ψ(λ)
(Bruce et al., 2001):
)(1
)(,a
b
aba
(2-2)
where a and b are positive real numbers for CWT. a represents the scaling factor
defining the width of the wavelet and b is the shifting factor determining the
position. The output of CWT is given by:
dffbaW babaf )()(,),( ,,
(2-3).
Given any specific scale ai (i=1, 2, ..., m, m is the maximum scale available), the
continuous wavelets can be shifted through any waveband and the CWT of a
reflectance spectrum generates a 1×n vector of wavelet coefficients. The CWT
coefficients (Wf(ai,bj), i=1, 2, ..., m, j=1,2,..., n) constitute a 2-dimensional
scalogram (i.e. a m×n matrix) where one dimension is scale and the other is
wavelength (or waveband). The value of each element of the scalogram represents
the wavelet power which measures the correlation between the scaled and shifted
mother wavelet and a segment of the reflectance spectrum and reflects the
similarity of the local spectral shape to a particular wavelet basis. Low scale
components of the scalogram capture absorption features of fine spectral details
and high scale components emulate the overall continuum of the reflectance
spectrum.
Leaf reflectance spectra contain specific absorption features from 350 to
2500 nm caused by the presence of pigments, water and dry matter. The shape of
the absorption features is similar to Gaussian or quasi-Gaussian function,
19
therefore, the second derivative of Gaussian (DOG) also known as the Mexican
Hat was used as the mother wavelet basis (Torrence & Compo, 1998) (Fig. 2).
Since the wavelet decomposition at a continuum of possible scales (i=1, 2, ..., m.)
would be computationally expensive and lead to a large data volume, the
dimensions of the scalogram was reduced by decomposing the reflectance spectra
at dyadic scales 21, 2
2, 2
3, ..., and 2
10 which are proportional to the effective length
of the wavelet compressed or stretched at that scale. Note that those scales are
labelled as scales 1 2 3 … and 10 in the following and still comparable to the
scales described in published studies by Blackburn & Ferwerda (2008) and Rivard
et al. (2008). The maximum scale available for the data of this study is 211
=2048
but this scale was discarded due to the low information content. All CWT
operations were accomplished in the IDL 6.3 Wavelet Toolkit (ITT Visual
Information Solutions, Boulder, CO, USA).
2.3.2. Statistical analysis of leaf pigment and water properties
The linear correlation coefficient between leaf pigment and water content
was examined for each dataset listed in Table 2-1. For each biochemical property,
a paired t-test was then performed on each dataset to evaluate the separability of
control and treatment (girdled and infested) samples. The resulting p-values were
used to determine the statistical significance of the observed separability (Zar,
1996). The datasets displaying control and treatment samples with distinct leaf
properties were then retained for subsequent wavelet analysis examining the
correlation between spectral and chemical properties.
2.3.3. Correlation scalograms
The continuous wavelet analysis converts each 1-D reflectance spectrum
to a 2-D wavelet power dataset which can be visualized as a scalogram with
dimensions of wavelength and scale and power represented as amplitude. In this
study, correlation scalograms (Fig. 2-3) were used to determine the wavelet power
features that most strongly correlate with the leaf properties investigated (Cocchi
20
et al., 2003). Each correlation scalogram reports the squared correlation
coefficient (R2), ranging in value from 0 to 1, at each wavelength and scale. R
2 is
obtained for the linear correlation established between wavelet power and an
independent variable across all measurements of a given dataset (e.g. combined
control and treatment). To build the correlation scalogram the control and
treatment (e.g. girdled or infested) data were combined to achieve a larger sample
size. In doing so, there were concerns that the dependence of control and
treatment samples might violate the statistical assumption of randomization for
observations within a sample. The dependence between the wavelet power and
water content of control and treatment samples was examined and no significant
correlation was observed.
In this study, the independent variables examined include the
concentration of total chlorophyll, leaf water content, and class ID, the latter
being used to identify features that distinguish the control and treatment samples.
Fig. 2-3 provides an example correlation scalogram for the leaf water content and
spectra of August 14 2008. Areas of the scalogram highlighted in blue on Fig. 2-3
display the most significant correlation and were selected as described in the next
section. Scalogram outputs from the wavelet analysis were computed for 10
scales and thus are not convenient for visualization. To facilitate the visual
inspection of scalograms, values at each scale were replicated or interpolated
resulting in resized scalograms (100×2151) that have a 10 times vertical
exaggeration. The interpolated scalograms were resampled with a cubic
convolution providing a smoother appearance that was used strictly for
visualization of features (Fig. 2-3A). The replicated scalograms (Fig. 2-3B) have a
rough appearance preserving the original data and were used for determining the
location of features selected as described in the next section.
2.3.4. Feature selection using correlation scalograms
Each element of a correlation scalogram represents a feature characterized
by a R2
value, wavelength and scale. The selection of the most informative
features for a given independent variable involved two steps: 1) retaining features
21
where the correlations are statistically significant (p<0.05), and 2) sorting these
features in descending order of R2
value to retain those encompassing the top 1%
of R2 values (Fig. 2-4). These feature sets are highlighted in blue on Figs. 2-3, 2-6
and 2-7.
Fig. 2-5 provides a structured and labelled representation of the scalogram
list for the girdled and infestation datasets. A total of 21 correlation scalograms
were examined to produce 21 individual feature sets. Note that once a feature set
was defined for a given independent variable and spectral dataset, the intersection
of two feature sets could be established as a crossover feature set. For example,
from the intersection of feature sets by class ID and water for August 14, 2008
one can examine if features that allow separation of control and infested samples
by class ID are consistent with features that correlate with water content for these
samples.
2.4. Results
2.4.1. Leaf pigment and water properties
A summary of correlations between laboratory-measured leaf properties is
provided in Table 2-2. A weak correlation between total chlorophyll and water
content is observed for the girdled and control datasets. As expected, a strong
correlation is seen between total chlorophyll and carotenoid content for all
datasets. Therefore, the leaf carotenoid data were excluded from the following
analysis.
The results of the two-tailed paired student’s t-tests are summarized in
Table 2-3. Significant differences in water content are observed for the control
and treatment samples of the two girdled datasets (Jun18-2007 and Aug30-2007)
and two of the five infested datasets (Jul13-2008 and Aug14-2008). Significant
differences in chlorophyll content are only observed for the two girdled datasets.
For these four datasets, one-tailed t-tests (H0: control = treatment; HA: control >
treatment) resulted in the same significance and stronger statistical power (one-
tailed test not shown). The distinct chlorophyll and water content for the control
22
and treatment samples of the two girdled datasets suggests that girdled trees
suffered water and chlorophyll stress induced by the mechanical injury. However,
the trees infested by mountain pine beetle show evidence of a water deficit but no
significant reduction in chlorophyll. The absence of significant difference in water
content between control and infested samples in June likely results from the lack
of time for tree to develop a response. The lack of a response for September and
October remains unexplained. Subsequent analysis of leaf pigment, water, and
spectral properties were conducted on the two girdled datasets and the two
infested datasets where control and treatment samples were separable based on
leaf water content.
2.4.2. Continuous wavelet analysis of the girdled datasets
The correlation scalograms produced with the Jun18-2007 dataset are
displayed in Fig. 2-6A~E. Fig. 2-6A highlights features strongly sensitive to
chlorophyll concentration that are observed in the visible (VIS) (530-740 nm) and
in the shortwave-infrared (SWIR) (1990-2120 nm) regions at scales of 1 to 7. The
discrimination by class ID (Fig. 2-6B) highlights features found in the SWIR
(1550-2150 nm) at scales of 2 to 5 that distinguish the control and treatment
samples. Leaf water content was strongly correlated with a few features in the
near-infrared (NIR) (950-1230 nm) (Fig. 2-6C) and in the SWIR (1500-2400 nm)
at scales of 2 to 5. The intersection of features observed for class ID with those of
chlorophyll (Fig. 2-6D) and water (Fig. 2-6E) respectively results in features near
1990-2010 nm at scales of 4 to 5 and near 1560-2150 nm at scales of 3 to 5. These
findings suggest that the significant differences in total chlorophyll and water
between the two groups of samples derived from t-tests (Table 2-3) are detected
in the CWT representation of spectral data. Scales of 4 and 5 are in general the
most frequently selected. The location of features is listed in Table 2-4.
Fig. 2-6F~J shows the resultant correlation scalograms produced for the
Aug30-2007 dataset. Generally, the locations of features selected are similar to
those of Jun18-2007 but there are more features at low scales. In the case of water
(Fig. 2-6F) several narrow feature regions are observed in the visible region that
23
are absent in the June dataset. The features are generally concordant with broader
feature regions observed for chlorophyll (Fig. 2-6H) and likely result from the
significant correlation between leaf water content and chlorophyll concentration
(r=0.57, p≤0.001 n=32) (Ceccato et al., 2001). The intersection of features
selected from the class ID scalogram with those of the chlorophyll (Fig. 2-6J)
scalogram shows no concordance with the feature set observed for the June
dataset (Fig. 2-6D). For the feature intersection of water and class ID (Fig. 2-6I),
features observed in June (Fig. 2-6E) do not align with those of August but a
number of features occur in the same spectral region.
Fig. 2-6K displays the class ID features common to the June and August
2007 datasets indicating that girdled and control samples can be distinguished
with two feature regions observed between 1560-2150 nm at scales 3, 4 and 5. As
indicated above a number of water features occur in these spectral regions for
both datasets (Fig. 2-6E and I).
Table 2-4 summarizes the wavelength regions and scales of the features
selected from the intersection of class ID features with those observed for
correlation scalograms of water and chlorophyll. It is worth noting that features
from scale 3 and 4 are common and features from scale 5 are consistently
selected. Ferwerda & Jones (2006) also found that features at this scale were
optimal for the prediction of leaf nitrogen concentration. These three scales
appear to represent the optimal combination of scales of decomposition for the
detection of changes in water and chlorophyll content in the girdled data. The
August dataset produced more chlorophyll features for the class ID separation
(Fig. 2-6J) than the June dataset (totalAugust=41, totalJune=3), but less water features
(totalAugust=40, totalJune=128). The increased capability to detect chlorophyll
deficit later in the growing season may be attributed to the presence of a
chlorophyll stress following water stress.
2.4.3. Continuous wavelet analysis of the infested datasets
The correlation scalograms produced with the Jul13-2008 dataset are
shown in Fig. 2-7L~O. Features strongly correlated to chlorophyll concentration
24
are not consistent in their wavelength location for both dates (Fig. 2-7L and R)
and span the complete spectral region. A number of features observed for July
have similar characteristics to those observed for June for the girdled dataset (Fig.
2-6A). For the Aug14-2008 dataset the chlorophyll features are primarily selected
at high scales. The absence of intersection features between chlorophyll and class
ID features for both infested datasets (Fig. 2-5) is consistent with the lack of
statistical difference in chlorophyll between control and infested samples (Table
2-3). The results from the wavelet analysis and statistical test reveal the difficulty
in separating control and infested samples based on chlorophyll abundance or
spectral indicators of chlorophyll.
For the July and August 2008 data, features for the class ID (Fig. 2-7M
and Q) and water (Fig. 2-7N and P) scalograms were found primarily in the NIR
and SWIR regions. Both dates share a well defined feature region near 1310-
1390nm (Fig. 2-7U) for class ID discrimination spanning multiple scales of which
a narrower region (1318-1322 nm) of limited scale is attributed to water for both
dates (Fig. 2-7T).
Table 2-5 summarizes the locations of features selected from the
intersection of scalograms for both infested datasets. In contrast to the girdled
datasets, more features are obtained from high scales with the infested datasets
(e.g., scale 7 and 8). While the number of water features that might be used to
distinguish control and infested samples declines from July to August
(totalJuly=74, totalAugust=14), there are five features at scale 7 between 1318-1322
nm that are common to both datasets. Finally the class ID features common to
both infested datasets (Fig. 2-7U) occur in a distinct region from the two key
feature regions identified for the girdled datasets (Fig. 2-6K).
2.5. Discussion
2.5.1. Regression models for the infested datasets
The analysis of the scalograms has highlighted a narrow spectral region
(1318-1322 nm) sensitive to needle water content that can be used to distinguish
25
needles of infested and control trees sampled in July and August. In this section
the correlation and data distribution of water content with wavelet power at 1320
nm and scale 7 is examined (Fig. 2-8A). For August, a linear regression model
shows a R2 value of 0.49 and RMSE of 7.84% while for July the accuracy is
lower (R2=0.40; RMSE=9.77%). The slope and the intercept of the regression
models for both dates are similar (Fig. 2-8A). These findings indicate that the
feature at 1320 nm is consistently sensitive to needle water content for this part of
the growing season. Fig. 2-8B and C provides a view of the distribution of the
control and infested samples within each dataset. For both dates the infested
samples span a wider range of water content and lower values than the control
data as expected. Thus the regression for the infested samples is a closer match to
that observed for the entire data (Fig. 2-8A). Infested samples for August provide
the highest R2 and lowest RMSE (6.93%). A paired t-test for control and infested
samples showed that the mean wavelet power at 1320 nm for scale 7 was
significantly different for both July and August (July: t = -2.8419, p = 0.0131;
August: t = -3.1684, p = 0.0081).
2.5.2. Selection of scales for scalograms
Scale 7 is found to be promising for green-attack detection whereas recent
studies have suggested that scales 5 and 6 are optimal for nitrogen and
chlorophyll estimation (Blackburn & Ferwerda, 2008; Ferwerda & Jones, 2006).
These differences are tied to the width of absorption features in spectra, the water
absorption near 1400 nm being relatively broad and thus better captured at a large
scale. In this study the CWT was conducted for 10 scales even though a greater
number of scales were permitted for the 2151 spectral bands of the data. The
wavelet signature at the highest scales can suffer from zero-padding during CWT
calculation (Torrence & Compo, 1998) and do not always provide reliable
information. For example, the features observed at scale 10 near 1550 nm for
chlorophyll in Fig. 2-6R are not considered to be relevant to chlorophyll
absorption (Curran, 1989). The lowest scale can capture high frequency
components of the input signal and thus tend to capture noise. Therefore, a
26
filtering of scales may facilitate the selection of significant features. In this study
few features in scale 1 were selected (12 of 496, Tables 2-5 & 2-6).
2.5.3. Wavelength regions of selected features
Previous studies by Ahern (1988) and Runesson (1991) examined visible
and near infrared spectra of healthy and infested trees reporting that significant
differences could be observed in the visible and red edge regions. In this study the
most significant and consistent spectral features attributed to changes in water
content were detected in the short wave infrared region. In the case of the infested
data set, all the features selected (Table 2-5) can be related to known water
absorptions in leaves located at varying distances from the nominal band centers
at 980, 1200, 1440, and 1920 nm. The results for the girdled data are more
difficult to interpret given the greater number and diversity of feature regions
detected for both dates. In this case features are not only observed near known
water absorptions but are also observed near 490nm, 660nm and 2300nm as seen
in August. The first two of these regions also produced features that correlated
well with total chlorophyll in August (Table 2-4). The considerably lower needle
water content observed for the girdled trees as opposed to the infested trees (Table
2-7) may suggest significantly greater water stress for the girdled trees and
explain the detection of features in the visible that correlate with water as well as
chlorophyll. These observations are consistent with the significant correlations
observed between leaf water and chlorophyll content for both dates of the girdling
experiment (Table 2-2), correlations that are not observed for the infested
datasets. The differing response of girdled and infested trees appears to indicate
that the girdling process does not provide a perfect simulation of the effects
caused by beetle infestation.
2.5.4. Implications for airborne detection of MPB infestation
In a study of hemlock abundance decline in the Catskills, USA, Pontius et
al. (2005) used an index (R970/R900nm) applied to AVIRIS airborne imagery to
27
detect leaf water content. In this study the 970 nm feature was not found to be
significantly correlated with water and a feature near 950nm correlated
significantly with water only for July. However this study has revealed the
presence of a narrow feature region (1318-1322 nm) for the detection of water
stress occurring during green attack and observed in July and August. There are
several implications of these findings for the potential airborne detection of green
attack. It remains to be determined if the successful detection obtained at the leaf
level study can be repeated at the canopy scale. The literature suggests that the
detection of water content is enhanced from the leaf to the canopy level (Sims &
Gamon, 2003). In this study needle stacks were measured as opposed to
individual needles thus the measurements may already reasonably capture the
spectral properties that would result from canopy scale observations particularly if
the spatial resolution was commensurate with the dimensions of observed tree
crowns (e.g. < 1.5 m).
The location of the key features on the edge of a strong atmospheric water
absorption may negatively impact the use of these features for detection of green
attack from airborne data but this remains to be evaluated. Negative effects would
include reduced signal to noise quality of the data and the likely requirement for a
rigorous atmospheric correction of the imagery (Asner et al., 2008; Clark et al.,
2005; Kokaly et al., 2003). However the use of continuous wavelet analysis is
well suited for the detection of key information because the noise component of
the signal can be filtered by removal of low scale wavelets which in this study
have not shown to incorporate key information for the detection of green attack.
Fig. 2-8B and C show that there is considerable overlap in the wavelet
power data distribution of infested and control samples though the means of both
groups are different. This observation would certainly preclude the separation of
both groups with a high accuracy. It may be feasible to establish a threshold that
would distinguish a substantial percentage of both populations, but a larger data
set would be needed to facilitate this analysis.
28
2.5.5. Potential improvements
This study revealed the detection of infested trees for two sites
investigated in July and August. The small number of sites provides a limited
perspective for the potential detectability of green attack at the canopy scale. The
results are certainly encouraging in that detection was possible and the lack of
detection early in the season (e.g. June) could have been a function of the growing
conditions such as moisture availability at the selected sites. A greater number of
sites spanning a range of growing conditions are needed to assess any dependence
of detection capability on specific growing conditions. The lack of detection in
June may also indicate that trees have not had a chance to respond thus limiting
the time span for detection.
The study established the correlation of features with class ID using
wavelet analysis for the detection of infested trees. However, it has not provided
an accuracy assessment of the class ID separation. The relatively small number of
sites and samples meant that all measurements were used to develop the model.
2.6. Conclusions
A remote early detection of mountain pine beetle infestation would be of
value to the monitoring and management of forests. Detailed spectral information
provided by reflectance measurements of needles collected in July and August
offer the potential for green-attack detection. Our work provides the following
conclusions:
The tree samples at the green-attack stage displayed measurable water stress
as did the girdled trees. While a deficit in total chlorophyll content was
documented for girdled trees, no chlorophyll deficit was observed for infested
trees. The deficits in chlorophyll and water content were also detectable from
the wavelet analysis of the reflectance data.
A number of spectral features were defined to distinguish girdled and infested
trees from healthy control trees. In general, the water features for the infested
datasets occupied narrower spectral intervals. For the girdled trees, features
attributed to changes in needle water content differed for June and August
29
(2007) and the majority were located in the SWIR region (1550-2370 nm)
across scales 1 to 5. For the July and August (2008) datasets of infested trees,
comparable water features were observed in the NIR and SWIR regions (950-
1390 nm) from scales 1 to 8.
Five features in the NIR (1318-1322 nm) spectral region at scale 7 were
consistently found in the July and August datasets of infested trees and can be
used to discriminate infested trees from healthy trees. These features are
located on the edge of a strong water absorption centered at 1450 nm. Their
spectral location and occurrence in the dataset of both dates imply they are
the most promising features for green-attack detection. These features occur
at longer wavelength than the range of wavelengths investigated in previous
studies by Ahern (1988) and Runesson (1991).
Considering the effect of viewing geometry and canopy structural
variability, it is unclear if the most persistent features could be enhanced or
negatively impacted at the canopy level if measured with airborne hyperspectral
systems.
30
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36
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37
Table 2-1. Description of sample size for each dataset
Treatment Dataset No. of pairs No. of trees
Control & girdled Jun18-2007
Aug30-2007
16
16
32
32
Control & infested Jun05-2008
Jul13-2008
Aug14-2008
Sep20-2008
Oct14-2008
15
15
13
13
12
30
30
26
26
24
If no green needles were available from a non-control tree, then the corresponding control
tree was not sampled. The lower number of trees sampled for the infested datasets was
caused by the inaccessibility of branches and the mortality of trees.
38
Table 2-2. Correlation coefficient (r) between chemical properties derived from
the Lodgepole Pine needle samples
Treatment Dataset chl vs water chl vs car
Control & girdled Jun18-2007
Aug30-2007
0.41 *
0.57 **
0.94 ***
0.96 ***
Control & infested Jun05-2008
Jul13-2008
Aug14-2008
Sep20-2008
Oct14-2008
-0.13 ns
0.10 ns
-0.20 ns
-0.35 ns
N/A
0.89 ***
0.95 ***
0.94 ***
0.86 ***
N/A
Decimal values are correlation coefficients r. Significance is: ns = not significant
(p>0.05), * p≤0.05 ** p≤0.001 *** p≤0.0001. car = carotenoid; chl = total chlorophyll.
The Oct14-2008 dataset only has measurements of water content.
39
Table 2-3. p-values of two-tailed paired student’s t-test results for control and
treatment samples for each dataset
Treatment Dataset Chl Water
Control vs. Girdled Jun18-2007 0.0019 0.0004
Aug30-2007 0.0001 0.0003
Control vs. Infested Jun05-2008 0.3985 0.3741
Jul13-2008 0.3674 0.0490
Aug14-2008 0.7968 0.0320
Sep20-2008 0.3784 0.5222
Oct14-2008 N/A 0.5610
p-values in bold indicate the significance at p≤0.05.
40
Table 2-4. Properties of features selected from the intersection of correlation
scalograms for the girdled datasets
Dataset Wavelengths (nm) and scales R2 [min, max]
1st variable 2
nd variable
d. June:
Class ID ∩ chl
S4: 1997-1998 (2)
S5: 2004 (1) (total = 3)
[0.35, 0.55] [0.37, 0.55]
e. June:
Class ID ∩ water
S3: 1570-1593 (24)
S4: 1572-1593, 1993-1998,
2097-2119 (51)
S5: 1995-2006, 2102-2142 (53)
(total = 128)
[0.35, 0.55] [0.29, 0.47]
i. August:
Class ID ∩ water
S1: 490, 2131 (1)
S2: 660-661, 1559-1560,
1595-1599, 1704-1705 (11)
S3: 570-571, 1561-1569,
1595-1598 (15)
S5: 2351-2363 (13) (total = 40)
[0.33, 0.51] [0.17, 0.40]
j. August:
Class ID ∩ chl
S1: 489-490, 657-660, 2131 (7)
S2: 657-661, 1596-1598 (8)
S3: 1595-1599 (5)
S5: 594-602 (9)
S7: 717-728 (12) (total = 41)
[0.33, 0.51] [0.20, 0.33]
k. Class ID:
June ∩ ugust
S3: 1562-1574, 1582-1601 (33)
S4: 1568-1597, 2102-2128 (57)
S5: 2099-2142 (44) (total = 134)
[0.35, 0.55] [0.33, 0.51]
1 2 … 8 refers to the scale of the wavelet decomposition. Values in parentheses are
the number of features selected at that scale. The total number of features summed for all
scales are shown following the last scale. Chl = chlorophyll. R2 [min, max] are the
minimum and maximum values of R2 for the selected features of individual variables
(e.g., class ID, water, chl).
41
Table 2-5. Properties of features selected from the intersection of correlation
scalograms for the infested datasets.
Dataset Wavelengths (nm) and scales R2 [min, max]
1st variable 2
nd variable
o. July:
Class ID ∩ water
S1: 1142 (1)
S3: 954-956 (3)
S4: 953 (1)
S7: 1316-1340 (25)
S8: 1335-1378 (44) (total = 74)
[0.19, 0.42] [0.35, 0.54]
s. August:
Class ID ∩ water
S1: 1743-1744 (2)
S2: 1141, 1388-1390 (4)
S3: 1388-1390 (3)
S7: 1318-1322 (5) (total = 14)
[0.17, 0.40] [0.48, 0.71]
t. o ∩ s S7: 1318-1322 (5) (total = 5)
See o and s See o and s
u. Class ID:
July ∩ ugust
S1: 1141 (1)
S2: 1388-1390 (3)
S3: 1388-1391 (4)
S4: 1385-1390 (6)
S5: 1376-1383 (8)
S6: 1362-1370 (9)
S7: 1315-1340 (26) (total = 57)
[0.17, 0.40] [0.19, 0.42]
42
Table 2-6. Summary of leaf water content (%) for four datasets with significant
differences between control and treatment samples.
Dataset Treatment Min Max Mean ± S.D.
Jun18-2007 Control 79.70 102.51 92.52 ± 6.07
Girdled 76.48 96.82 83.76 ± 5.86
Aug30-2007 Control 99.92 134.57 113.16 ± 8.32
Girdled 92.06 109.66 100.91 ± 4.98
Jul13-2008 Control 107.70 142.94 129.81 ± 10.35
Infested 101.18 146.12 120.10 ± 13.53
Aug14-2008 Control 114.34 143.27 128.91 ± 9.34
Infested 96.51 138.72 120.10 ± 11.38
43
Fig. 2-1. Locations of the study sites in Alberta, Canada.
44
Fig. 2-2. Mexican Hat wavelets of scales 5 and 6 draped on a reflectance spectrum
of healthy needles. The wavelet of scale 5 is an approximate match for the
wavelength width of the green peak and the reversed wavelet of scale 6 is a
reasonable match for the width of a major water absorption center. This feature
and the green peak would be captured by wavelets of scale 6 and 5, respectively.
45
Fig. 2-3. Visualization of scalograms: (A) Scale interpolated; (B) Scale replicated.
Scalograms were produced with the Aug14-2008 dataset (water features shown in
blue). Wavelength is displayed along the horizontal direction and scale along the
vertical axis. The R2 value at each wavelength and scale is displayed as amplitude
or brightness.
46
Fig. 2-4. Example of the frequency distribution of R2 values observed for the
scalogram in Fig. 2-3B. The cut-off R2 value used to delineate features correlated
to biochemical properties or class ID is defined by the highest R2 values
encompassing 1% of the data.
47
Fig. 2-5. Structure and labeling of feature sets derived from correlation
scalograms indexed alphabetically from A to U. For example, the feature set A is
derived from the correlation scalogram for the independent variable chlorophyll
and the dataset Jun18-2007; D. A ∩ B refers to feature set D obtained by the
intersection of feature set A and feature set B; E ∩ I = indicates that the
intersection of feature set E and feature set I is an empty set.
48
Fig. 2-6. Correlation scalograms A-K listed in Fig. 2-5 for the girdling datasets.
The selected features are shown in blue on scalograms.
49
Fig. 2-7. Correlation scalograms L-U listed in Fig. 2-5 for the infested datasets.
50
Fig. 2-8. Relationships between water content and the wavelet power at 1320 nm
and scale 7 for the infested datasets: (A) combined control and infested data for
July and August, (B) control and infested for July, (C) control and infested for
August. The thicker solid and dashed lines in (B) and (C) are those seen in (A).
51
CHAPTER 3 – SPECTROSCOPIC DETERMINATION OF
LEAF WATER CONTENT USING CONTINUOUS WAVELET
ANALYSIS2
3.1. Introduction
Water is a fundamental chemical constituent of plants, and its abundance
in leaves is closely tied to leaf vigor, phylogenic traits such as leaf structure and
shape, and photosynthetic efficiency (Kramer & Boyer, 1995). Evaluation of plant
water status plays an important role in assessing drought stress, predicting
susceptibility to wildfire and monitoring the general physiological status of
vegetation stands Datt 1999 . ccurate retrieval of leaf water content via
remotely sensed data is a long-sought goal of the biological remote sensing
community Hunt ock 1989; Pe uelas et al., 1997).
Common methods for determining leaf water content include equivalent
water thickness (EWT) and gravimetric water content (GWC) (Datt, 1999). The
EWT expresses leaf water content in mass per unit leaf area (g/cm2), whereas the
GWC method employs a direct measurement that compares fresh leaf mass (with
intrinsic water) to dry leaf mass (without intrinsic water). In general, the GWC is
a preferred indicator of leaf water status when the measurement of leaf area is not
easily achieved, as is the case for conifer needles. The GWC, which indicates the
gravimetric proportions of water relative to other plant materials in leaves, can be
expressed as leaf water content either by dry weight (LWCD, %) or fresh weight
(LWCF, %). The LWCD is extensively used in fire risk modeling and is referred to
as the fuel moisture content (Chuvieco et al., 2002). The LWCF serves as a key
leaf trait in ecological studies (Garnier & Laurent, 1994).
2 A version of this chapter has been submitted as: Cheng, T., Rivard, B., Sánchez-
Azofeifa, G. A. Spectroscopic determination of leaf water content using continuous
wavelet analysis.
Author contributions: Dr. Sánchez-Azofeifa provided the dataset. Dr. Rivard input
critiques on the research. Dr. Rivard and Dr. Sánchez-Azofeifa discussed the results, and
provided editing comments on the manuscript. I organized the data, wrote the codes for
data processing, processed the data, interpreted the results, and composed the manuscript.
52
A number of studies have examined the empirical relationship of leaf
reflectance in the near infrared (NIR) and shortwave infrared (SWIR) regions
with leaf GWC or EWT (Ceccato et al., 2001; Danson et al., 1992; Danson &
Bowyer, 2004; Sims & Gamon, 2003). Some studies have compared the
estimation of GWC and EWT using leaf reflectance illustrating that GWC is
considerably more difficult to estimate than EWT (Table 3-1) (Danson & Bowyer,
2004; Datt, 1999; Li et al., 2007; Maki et al., 2004; Riaño et al., 2005).
Investigations estimating GWC from leaf reflectance report various strengths of
correlation (Table 3-1). Some studies use spectral indices that employ a NIR or
SWIR band to detect the leaf water content and a NIR band as a reference to
normalize the effect of leaf structural variability (Colombo et al., 2008; Danson &
Bowyer, 2004). Studies focusing on a single species (Dawson et al., 1998; Pu et
al., 2004; Tian et al., 2001) are likely less influenced by variability in leaf
structure and have achieved good predictions (Table 3-1, R2≈0.86 using neural
networks or a combination of bands. However, the knowledge gained from
studying either a limited number of plant species or a narrow range of GWC
values is difficult to apply to more complex datasets encompassing a diversity of
species or a wide range of GWC values. Riaño et al. (2005) investigated the
inversion of the PROSPECT radiative transfer model to indirectly estimate LWCD
of 37 species and obtained a poor estimation of LWCD due to the high uncertainty
in estimating DMC (R2 = 0.33). More recently, a combination of genetic
algorithms with partial least squares (GA-PLS, Li et al, 2007) regression was
proposed for the accurate estimations of LWCD of 37 species (R2 = 0.89).
However, these methods are computationally intensive and complex, and thus of
limited practical use.
Continuous wavelet analysis (CWA) is emerging as a promising tool in
laboratory spectroscopy for deriving biochemical constituent concentrations from
leaf reflectance spectra (Cheng et al. 2010; Blackburn, 2007; Blackburn &
Ferwerda, 2008; Ferwerda & Jones, 2006). The continuous wavelet transform
(CWT) provides a decomposition of leaf reflectance spectra into a number of
scale components and each component is directly comparable to the reflectance
53
spectra. In this study, I aim to extract wavelet features (coefficients) that are
sensitive to the change in GWC and insensitive to variations in leaf structural
properties across a wide range of species. Inherent to the good estimation of GWC
is the relationship of GWC to dry matter content (DMC), a topic that has received
little attention in studies aiming to estimate GWC from leaf reflectance. Kokaly &
Clark (1999) and Tian et al.(2001) noted that the spectral variation in the
shortwave infrared induced by increasing leaf GWC included not only a decrease
in the amplitude of reflectance but also changes in the depth and shape of
absorption features centered near 1730 nm and 2100 nm and attributed to leaf dry
matter. Continuous wavelet analysis is used in this study as a spectral feature
analysis tool to examine the changes in leaf spectral response as a function of
GWC and gain insights on the influence of water and DMC. Specifically, I seek to
answer two questions: (i) Is CWT more effective than the commonly used spectral
indices to estimate leaf GWC? (ii) What are the most informative wavelet features
to estimate leaf GWC? Do they provide new insights into spectral variation due to
changes in leaf water content?
3.2. Data set
3.2.1. Site description
Leaf samples were collected from two sites in the Republic of Panama.
The first site is located in a tropical dry forest of Parque Natural Metropolitano
(PNM) near the Pacific coast. This forest experiences a severe dry season from
mid-December until the end of April and has an annual rainfall of about 1,740
mm. The second site is located in a tropical wet forest of Fort Sherman (FS) on
the Caribbean coast. This ecosystem experiences a mild dry season from January
to March and has an annual rainfall of about 3300 mm. Construction cranes
owned by the Smithsonian Tropical Research Institute (STRI) were used at both
sites to access the top of the canopy and collect leaf samples (Castro-Esau et al.
2004).
54
3.2.2. Data collection
At PNM, leaves were collected from 23 species of lianas and eight species
of trees. At FS, eight species of lianas and eight species of trees were sampled.
Collection of leaves took place in March 2007. All samples consisted of sun
leaves.
Clipping of leaves and handling protocols were followed as described in
Sánchez-Azofeifa et al. (2009). Reflectance measurements were recorded between
350 and 2500 nm with a FieldSpec® FR spectroradiometer (ASD Inc., Boulder,
CO, USA). The instrument provides a resolution of 3 nm at 700 nm, 10 nm at
1500 nm, and 10 nm at 2100 nm. Five or ten leaf samples were collected per
species and a total of 265 leaf samples were collected for the 47 species. Three
reflectance spectra were taken per leaf using an ASD leaf clip covering a halogen
bulb-illuminated area with a radius totaling 10mm. From these measurements, a
mean reflectance spectrum was calculated for each leaf. The leaf water content
was estimated by comparing the weight of the fresh leaf the leaf’s total mass less
than one hour after clipping) and the mass of the same leaf after a three-day
drying period at 60oC.
3.3. Methods
3.3.1. Estimation of leaf gravimetric water content
Gravimetric water content in leaves was estimated using the following
expressions:
(3-1)
(3-2)
where FW is the leaf fresh weight and DW is the dry weight. As the amount of
water may exceed the leaf dry weight, some measurements of LWCD were over
100% but all measurements of LWCF were less than 100%. A summary of LWCD
55
and LWCF measurements is provided in Table 3-2. The two GWC expressions are
convertible by:
(3-3)
(3-4)
his study’s LWCD or LWCF value range exceeds the range reported in all similar
studies, with the exception of studies investigating the LOPEX data (Table 3-1)
(e.g. Danson & Bowyer, 2004). This sizeable range correlates to the wide range of
species examined in this study, species that span both dry and wet tropical forest
environments.
3.3.2. Wavelet analysis
Wavelet analysis is an effective signal-processing tool that functions by
decomposing the original signal into multiple scales (Mallat, 1989). In the last
two decades, wavelet analysis has been intensively explored for applications in
medicine and biology (Addison, 2005; Unser & Aldroubi, 1996), chemistry
(Leung et al., 1998) and geophysics (Farge, 1992; Torrence & Compo, 1998). In
remote sensing, the wavelet analysis approach is widely applied to multispectral
satellite imagery for image fusion (Gonz lez- ud cana et al., 2004; Núñez et al.,
1999; Shi et al., 2003; Zhang & Hong, 2005; Zhou et al., 1998) and texture
classification (Arivazhagan & Ganesan, 2003; Laba et al., 2007; Myint et al.,
2004; Ouma et al., 2008). Wavelet analysis is a promising method for processing
hyperspectral signatures and has been successfully applied to hyperspectral data
for dimensionality reduction (Bruce et al., 2002; Kaewpijit et al., 2003). Recent
studies have compared the advantages of wavelet analysis to more conventional
methods for identifying plant species (Kalácska et al., 2007; Koger et al., 2003;
Zhang et al., 2006) and for estimating forest biophysical parameters (Pu & Gong,
2004) by means of hyperspectral imagery.
56
Wavelet transforms include two variations: the discrete wavelet transform
(DWT) and the continuous wavelet transform (CWT) (Blackburn & Ferwerda,
2008; Bruce et al., 2001). The former method is mostly used for data compression
and feature extraction/reduction, but the latter is preferred to generate a more
readily interpretable multi-scale representation of signals (Bruce et al., 2001; Du
et al., 2006). The DWT wavelet coefficients, after transformation, are difficult to
interpret and require an inverse discrete wavelet transform for comparison with
the original reflectance bands (Kalacska et al., 2007). In contrast, each CWT
wavelet coefficient is directly comparable to a reflectance band and thus provides
substantially more information on the shape and position of absorption features in
leaf spectra (Blackburn & Ferwerda, 2008).
3.3.3. Continuous wavelet transform (CWT)
The CWT is a linear operation that uses a mother wavelet function to
convert a hyperspectral reflectance spectrum f(λ) (λ=1, 2,..., n, n is the number of
wavebands and n=2151 herein) into sets of coefficients. Mathematically, the
continuous wavelets ψa,b(λ) are produced by scaling (dilating) and shifting
(translating) the mother wavelet ψ(λ) (Bruce et al., 2001):
)(1
)(,a
b
aba
(3-5)
where a and b are positive real numbers. a represents the scaling factor defining
the width of the wavelet and b is the shifting factor determining the position. The
output of CWT is given by (Mallat, 1991):
(3-6)
where is the complex conjugate of
3.
3 Note that complex conjugation changes the function only if a complex wavelet function such as
Morlet function is used. The derivatives of Gaussian function are real functions.
57
For all scales of decomposition, the CWT coefficients (Wf(ai,bj), i=1, 2, ..., m,
j=1,2,..., n) constitute a 2-dimensional scalogram (i.e. a m×n matrix) of which one
dimension is scale 1 2 … m) and the other is wavelength (or waveband, 1, 2,
… n). Each scale component of the scalogram is of the same length as the
reflectance spectrum and this representation is readily interpretable. Low scale
components are suitable to capture the characteristics of narrow absorption
features and high scale components are well suited to define the overall spectral
shape of leaf spectra (Blackburn & Ferwerda, 2008; Ferwerda & Jones, 2006;
Rivard et al., 2008). The wavelet power, which refers to the magnitude of each
wavelet coefficient, measures the correlation between the scaled and shifted
mother wavelet and a segment of the reflectance spectrum and reflects the
similarity of the local spectral shape to the mother wavelet (Rivard et al., 2008). It
can be used to identify the change in shape and depth of absorption features
across spectra and record the spectral variation introduced by changes in GWC.
A typical leaf reflectance spectrum in the 350-2500 nm range consists of a
background continuum on which a number of absorption features attributable to
pigments, water and dry matter are superimposed (Curran, 1989). Previous
research suggests that the shape of the absorption features is similar to Gaussian
or quasi-Gaussian function (Miller et al., 1990) or a combination of multiple
Gaussian functions (le Maire et al., 2004). Therefore, the second derivative of
Gaussian (DOG) also known as the Mexican Hat was used as the mother wavelet
basis (Torrence & Compo, 1998). The effective support range of the Mexican Hat
is [-5, 5] for the scale a=1 and [-5a1, 5a1] for a=a1 (Du et al., 2006). The width of
a scaled wavelet (10a1) determines the number of wavebands that are to be
convolved with the wavelet and attributed to the wavelet coefficient. Since the
wavelet decomposition at a continuum of possible scales (i=1, 2, ..., m.) would be
computationally expensive and lead to a large data volume, the dimensions of the
scalogram were reduced by decomposing the reflectance spectra at dyadic scales
21, 2
2, 2
3, ..., and 2
10. For a simple representation of the scalograms, those scales
are labeled as scales 1 2 3 … and 10 in the following section and are
comparable to the scales described in related studies by Blackburn & Ferwerda
58
(2008) and Rivard et al. (2008). For the leaf reflectance spectra from the ASD
Fieldspec Pro spectrometer, there are 2151 bands available (350-2500 nm). Any
scale greater than 210
=1024 is discarded because the decomposed components at
higher scales do not carry meaningful spectral information. All CWT operations
were accomplished by means of the IDL 6.3 Wavelet Toolkit (ITT Visual
Information Solutions, Boulder, CO, USA).
3.3.4. Feature selection from correlation scalograms
To deal with the redundancy of wavelet features caused by continuous
decomposition, a feature-selection technique is required to identify the most
important features used to derive the GWC. The method to select meaningful
wavelet features comprises four main steps (Fig. 3-1). At Step 1, CWT was
applied to all reflectance spectra to calculate the wavelet power as a function of
wavelength and scale. Therefore, the wavelet data resulting from each spectrum
were stored as a wavelet power scalogram with dimensions of power, wavelength,
and scale. To identify features sensitive to variations in GWC, a correlation
scalogram was constructed at tep 2 by establishing the Pearson’s linear
correlations between each element of wavelet power scalograms and GWC of all
leaf samples. The correlation scalogram reports a squared correlation coefficient
(R2), ranging in magnitude from 0 to 1, at each wavelength and scale. Each
element of the correlation scalogram represents a feature that could be selected.
At Step 3, the features where R2 is not statistically significant (p>=0.05) were
masked. The remaining features were then sorted in descending order of R2, and a
threshold R2 was applied to delineate the top 1% features that most strongly
correlated with GWC. These features delineated by the threshold formed a
number of scattered feature regions on the correlation scalogram (Fig. 3-2).
Because features within each region were produced at consecutive wavelength
positions and scales, they carried redundant spectral information. At step 4, the
feature with the maximum R2 within each region was determined to represent the
spectral information captured by the feature region and expressed as (wavelength
59
in nm, scale). Eventually, a small number of sparsely distributed features were
selected representing these regions and capturing the most important information
related to changes in leaf water content.
3.3.5. Spectral indices
Three commonly used spectral indices (Table 3-3) designed to estimate
vegetation water content were calculated to test their usefulness for estimating
leaf GWC for the 47 tropical forest tree and liana species included in this study.
The moisture stress index (MSI) was developed by Hunt et al. (1986) and further
investigated by Hunt & Rock (1989) to relate leaf reflectance with leaf elative
Water Content WC . he normalized difference water index NDWI was
originally proposed by Gao 1996 to remotely sense the EW at the canopy
level. he water index WI was originally designed by Pe uelas et al. (1997) to
relate LWCD with leaf reflectance spectra across species.
3.3.6. Calibration and validation of regression models
The entire dataset, consisting of reflectance spectra and leaf water content
for 265 leaf samples, was split into two parts, with 60% of the data assigned to the
calibration of regression models and 40% used for validating the models. The
splitting led to 3 (or 6) samples per species in the calibration set and 2 (or 4)
samples per species in the validation set. Suitable wavelet features were identified
from the measurements in the calibration set using the method described in
Section 3.4. Linear functions were applied to the calibration data to model the
relationship between water content and wavelet features or spectral indices. For
the wavelet approach, both individual and combinations of multiple spectral
features were examined to calibrate the predictive models. Prior to combining
features a stepwise selection based on kaike’s Information Criterion IC
(Estes et al., 2008; Venables & Ripley, 2002; Zhou et al., 2006) was applied to
determine the features that should be included in the model. Coefficients of
60
determination (R2) and p-values were derived from analyses of data to assess how
well the linear regressions corresponded to the calibration set. Calibrated models
were then applied to the validation set and their predictive capabilities were
assessed based on the predictive coefficient of determination (R2) and the root
mean square error (RMSE) between the measured and predicted water content.
3.4. Results
3.4.1. Response of leaf reflectance to variations in leaf water content
In Fig. 3-3, associations between five reflectance spectra and various
LWCD values are displayed. These associations illustrate the spectral variation in
the 350-2500 nm range caused by changes in leaf water content. As LWCD
decreases from the highest (418.18%) to the lowest (32.31%) value, the strong
water absorption features at 1445 nm and 1930 nm become weaker, and the
amplitude of the reflectance spectrum in the SWIR region increases. In addition,
the absorption features in the 1670-1830 nm and 2000-2200 nm regions, which
have been found to correspond to leaf dry matter constituents (e.g., protein, lignin
and cellulose) (Elvidge, 1990; Kokaly & Clark, 1999), become more apparent
with decreasing LWCD. In particular, the absorption centered in the 1670-1830
nm shifts towards shorter wavelength regions, and the spectral shape observed
from 2000 to 2200 nm changes gradually from convex to concave as LWCD
decreases. Below, I illustrate that the wavelet analysis extracts information
pertaining to water by capturing the aforementioned changes in overall amplitude
and spectral shape.
3.4.2. Correlation of water indices with leaf water content for a wide
range of species
Fig. 3-4 displays the linear regression models for spectral indices (Table 3-
3) and water content expressed as LWCD and LWCF. MSI displays the weakest
correlation (LWCD: R2 = 0.05; LWCF: R
2 = 0.08). Low values of R
2 are observed
61
for the three indices (R2 from 0.05 to 0.12) either for LWCD or LWCF. Most of
the values of spectral indices were scattered vertically, indicating that these
indices were not effective to capture the change in leaf water content for the wide
range of plant species.
3.4.3. Most informative wavelet features to estimate leaf water content
Using continuous wavelet analysis of reflectance spectra, eight wavelet
features (one per feature region) were extracted from the correlation scalogram
for LWCD. Similarly, eight wavelet features were extracted from the correlation
scalogram for LWCF. Regression models indicated that all extracted features
significantly correlated to water content (p<0.0001). This represents an R2
improvement of at least 0.3 over the values derived from linear regressions
(R2>0.40) obtained using spectral indices (Table 3-4). For LWCD, the strongest
correlation was produced by the wavelet power at 2165 nm at scale 4 (R2 = 0.62)
and the weakest by the wavelet power at 2227 nm at scale 3 (R2 = 0.43).
Wavelength locations of all extracted features for LWCF were similar to those for
LWCD and the minimal differences were within the sampling uncertainty (10 nm)
for the SWIR region of the spectrometer. The magnitude of R2 values for LWCF
features (R2 from 0.51 to 0.69) were higher than those for corresponding LWCD
features. The two groups of features differed in the ranking of R2.
All wavelet features correlating with LWCD and LWCF are observed in the
SWIR region (Fig. 3-5; LWCF features are not shown because these are roughly
equivalent to LWCD features). Two high-scale features (1343nm, 7) and (1869nm,
6) (Table 3-5) occur on the left shoulder of two strong water absorption features
(Fig. 3-5). The remaining features, primarily caused by leaf dry matter, occur at
low scales and relate to absorption regions centered at approximately 1730, 2100
and 2300 nm. Feature (1734nm, 4) lies near a lignin-cellulose absorption center
at 1730 nm, while features (2034nm, 3) and (2165nm, 4) are close to absorptions
indicative of proteins, centered at 2054 nm and 2172 nm, respectively (Kokaly &
62
Clark, 1999; Kokaly, 2001). These three absorption bands become more
prominent with decreasing water content in leaves.
The strongest relationship between leaf water content and wavelet power
for an individual feature is observed for feature (2165nm, 4) as shown in Fig. 3-6.
For LWCD, the relationship was linear up to a water content of approximately
250% after which it became asymptotic and the wavelet power became insensitive
to changes in leaf water content. This data pattern was observed for the eight
features listed in Table 3-4. This data pattern was not observed for LWCF (Fig. 3-
6), though LWCD with all other wavelet features showed similar relationships
(data not shown). Excluding those observations of LWCD above 250% led to a
slight increase of R2 by 0.02.
Models combining a number of features were then investigated. A
stepwise selection of regression models based on AIC suggested that the
combination of six features excluding (1579nm, 3) and (2227nm, 3) produced the
best model for LWCD with a R2 of 0.69 (I in Table 3-4). For LWCF, the best
model was produced with six features excluding features (1870nm, 6) and
(1576nm, 3). The reduced feature sets for LWCD or LWCF were then split into
high-scale and low-scale feature subsets for modeling, and higher R2 values were
found for low-scale feature sets (e.g. J in Table 3-4).
3.4.4. Prediction of leaf water content using the wavelet features
The regression models calibrated using LWCD and LWCF wavelet features
were applied to the validation set to determine the accuracy with which water
content could be estimated. Feature (2165 nm, 4) produced the most accurate
predictions of LWCD and LWCF, with RMSE values of 28.33% and 4.86%,
respectively (Table 3-6). LWCD and LWCF were best predicted using a linear
combination of six individual features resulting in a RMSE of 26.04% (R2 = 0.71)
and 4.34% (R2 = 0.75) respectively. The latter compares to the accuracy of LWCF
estimation reported by Asner & Martin (2008; Fig. 2).
63
The results obtained from applying the most accurate single feature and
multiple feature models (A & I in Table 3-6) to the validation set are shown on
Fig. 3-7. The data points for both models are scattered near the 1:1 line except for
LWCD values exceeding 250%. This poor sensitivity at high levels of water
content was also observed in the results of Danson & Bowyer (2004) where the
WI underestimated most of the LWCD observations ranging from 250% to 1400%
and the accuracy was much lower. Interestingly, this phenomenon was not seen
for the estimations and predictions of LWCF (Figs. 3-6, 3-7).
3.5. Discussion
I investigated the relationship between spectral properties and leaf water
content expressed as LWCD and LWCF for a diverse tropical species dataset
(Sánchez-Azofeifa et al. 2009). To the best of our knowledge, this investigation is
the first successful study linking the two measures of leaf water content to
reflectance spectroscopy.
3.5.1. Wavelet features for the estimation of leaf water content
The wavelet features used to estimate LWCD and LWCF were not
significantly different. Two high-scale LWCD features (1343nm, 7) and (1869nm,
6) were found on the leading edge of the two strongest water absorption bands,
and they captured the variations in amplitude of leaf reflectance over a broad
spectral interval. The remaining significant features (1734nm, 4), (2034nm, 3),
(2165nm, 4), and (2375nm, 4) that were found at low scales appeared away from
strong water absorptions and accounted for changes in the depth and shape of dry
matter absorption features. More information on LWCD was captured by the
variation in depth and shape of dry matter absorptions than by changes in water
absorptions. The use of CWT has facilitated the detection of dry matter absorption
features that are obscured by the presence of leaf water. Past studies by Danson &
Bowyer (2004) and Riaño et al. (2005) concluded that the presence of spectral
64
features due to dry matter similarly complicated the estimation of LWCD from
leaf reflectance spectra. However, the results of this study suggest that the
variable strength of dry matter absorptions in response to changes in leaf water
content in our data contributes significantly to the estimation of LWCD. Indeed,
the correlation of leaf water content with the dry matter wavelet feature (2165nm,
4) is the strongest among those observed for an individual feature in this study.
However, a combination of low-scale and high-scale features results in the best
leaf water content predictive capability.
3.5.2. Why do spectral indices not work?
The results confirm the difficulty in relating LWCD or LWCF to
commonly used spectral indices (Maki et al. 2004). One reason spectral indices
relate poorly to leaf water content could be the large spectral variability that arises
from the richness of species composition (Sims & Gamon, 2002). This has been
documented in a number of studies of tropical ecosystems (Castro-Esau et al.,
2006; Sánchez-Azofeifa et al., 2009). The poor sensitivity of MSI, WI and NDWI
to the changes in LWCD and LWCF may indicate that ratios and normalized
differential ratios are not effective in addressing the confounding effects of
variable leaf structural properties across a wide selection of tropical species. This
is not surprising given that MSI and NDWI were designed for the analysis of
multispectral data, and thus have limitations in terms of the optimization of the
location of bands that could be selected. WI may perform poorly because it was
fashioned from an investigation including only thirteen species. However, it is
likely that the spectral range (390-1100 nm) selected for the WI is the most likely
cause of the inconsistent results as our findings suggest that the key features
related to leaf water content are observed beyond 1100nm.
65
3.5.3. Advantages of the continuous wavelet analysis
This study presented CWA as an effective method for both analyzing the
spectra and selecting features for the estimation of leaf water content. Unlike
spectral indices that use ratios to normalize variations in the magnitude of
reflectance, CWA provides a multiscale representation of a reflectance spectrum
isolating absorption features at various scales from within the continuum. The
correlation scalogram resulting from the analysis of multiple leaf samples then
enables the optimal selection of spectral features most indicative of leaf water
(Fig. 3-2). Therefore, no ratios of wavelet power are necessary for normalization.
For example, the wavelet feature at (1579nm, 3) is a close match to the index
wavelength (1600 nm) of the MSI but it yields a stronger correlation to water
content (LWCD: R2
wp.(1579, 3) = 0.44, R2MSI = 0.05). The continuum removal
technique is also capable of isolating specific absorption features from the
continuum. CWA however, provides more robust information by using scaled
wavelets to separate narrow and broad absorptions into different scales. The
continuous displacement of the wavelet along the spectrum ensures that no
absorption features are omitted and that all absorption features are detected at one
time. The partial least squares (PLS) regression is comparable to CWA in
predictive performance, but it is a more difficult operation with complex
calibration requirements.
A small number of wavelet features are selected from the correlation
scalogram based on thousands of input reflectance bands. The number of features
extracted is dependent on the number of feature regions that are delineated on the
correlation scalogram (Fig. 3-2) by the adjustable percentage threshold. In this
study, a 1% threshold was utilized, since a smaller percentage threshold would
have reduced the number of feature regions. The feature selection process ensures
an optimization of wavelet features that correlate with leaf water content. The
multi-scale analysis of absorption features offers an opportunity to capture water
and dry matter absorptions that are manifested at different scales.
66
In a study aiming to determine the leaf water content (EWT) for a variety
of species, Danson et al., (1992) attempted to suppress the variations in leaf
internal structure by relating EWT to the first derivative of reflectance spectra.
Our results suggest that the decomposition of reflectance spectra with CWT also
effectively decreases the influence of leaf structural variation for the
spectroscopic estimation of LWCD and LWCF.
3.5.4. Improvements of leaf water content by dry mass (LWCD)
The data set of this study displays values of LWCD ranging from 32.3% to
418.2%. For values of LWCD exceeding 250%, our wavelet-based predictive
models display poor sensitivity to changes in LWCD (Fig. 3-6). This poor
sensitivity was also observed, but not discussed in the study of Danson & Bowyer
(2004; Fig. 5a) where LWCD values ranged from 9% to 1258% and
underestimation occurred for most observations above 250%. However, LWCF
with high levels of water content corresponded well to the predictions generated
by wavelet-based models (Fig. 3-7). I demonstrated that LWCF was more strongly
correlated to wavelet power than LWCD based on a linear fit. According to Eq. (3-
4), if LWCF is linearly related to wavelet power, then LWCD, which is a non-
linear function of LWCF, would have a non-linear relation to wavelet power (Fig.
3-8). Thus, non-linear functions (e.g., power, exponential) might be explicitly
employed to more completely describe the relationship between wavelet power
and LWCD over a wide range of values. However, the relatively low number of
samples in this study with a high water content (ten data points with
LWCD>250%) precludes a thorough investigation of non-linear functions. In
addition, ideally the water content would be more uniformly distributed across the
data set to explore such functions.
As an attempt to improve the estimation of LWCD, Eq. (3-4) was used to
transform the LWCF values predicted from the wavelet models shown in Fig. 3-7,
C and D. The corresponding LWCD estimates are shown in Fig. 3-9, A and B,
respectively. The indirect estimates of LWCD resulted in higher accuracies than
67
the direct estimates (Table 3-6) and the sensitivity at high water content levels
was slightly enhanced (Fig. 3-9). Using the best feature combination (I in Table 3-
6), the RMSE value of the indirect LWCD estimation decreased by 3% (from
26.04% to 23.04%) and the R2 value increased by 0.07 (from 0.71 to 0.78). The
transformation of LWCF to LWCD offers an opportunity to bridge the studies
estimating LWCF and LWCD from leaf reflectance.
3.6. Conclusion
This study has demonstrated the use of CWA applied to leaf reflectance
spectra for the accurate prediction of leaf water content expressed as percent of
dry mass (LWCD) and fresh mass (LWCF). A small number of wavelet features
were strongly correlated to LWCD and LWCF, whereas established spectral
indices were more poorly correlated. By decomposing the reflectance spectra into
various scales, CWA was shown to be effective in identifying meaningful spectral
information that relates to the estimation of leaf water content. The eight wavelet
features used to predict LWCD and LWCF were not significantly different, but the
predictive models were different. The method more accurately estimated LWCF
than it did LWCD, and LWCD values exceeding 250% tended to be
underestimated.
The wavelength positions of the eight wavelet features occur in the SWIR
region (1300–2500 nm). The high-scale features captured amplitude variations in
the broad shape of the reflectance spectra. The low-scale features captured
variations in the shape and depth of dry matter absorptions centered near 1730 nm
and 2100 nm. Our results provide new insights into the role of dry matter
absorption features in the SWIR region for the accurate spectral estimation of
LWCD and LWCF. The advantages of wavelet analysis over existing spectral
indices for the estimation of leaf water content should appeal to communities
interested in the accurate estimation of LWCD or LWCF particularly for
investigations of diverse ecosystems. The method developed for estimating leaf
water content is promising for determining leaf biochemistry from spectra and
68
may be extended to the estimation of chlorophyll, lignin, cellulose, and nitrogen
concentrations in ecosystem studies.
69
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features. International Journal of Remote Sensing, 22, 2329-2338.
Torrence, C., & Compo, G. P. (1998). A practical guide to wavelet analysis.
Bulletin of the American Meteorological Society, 79, 61-78.
Tucker, C. J. (1980). Remote sensing of leaf water content in the near
infrared. Remote Sensing of Environment, 10, 23-32.
Unser, M., & Aldroubi, A. (1996). A review of wavelets in biomedical
applications. Proceedings of the IEEE, 84, 626-638.
Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S.
Fourth edition. Springer.
Zhang, J. ivard . nchez-Azofeifa, A., & Castro-Esau, K. (2006). Intra- and
inter-class spectral variability of tropical tree species at La Selva, Costa Rica:
Implications for species identification using HYDICE imagery. Remote
Sensing of Environment, 105, 129-141.
75
Zhang, Y., & Hong, G. (2005). An IHS and wavelet integrated approach to
improve pan-sharpening visual quality of natural colour IKONOS and
QuickBird images. Information Fusion, 6, 225-234.
Zhou, J., Civco, D. L., & Silander, J. A. (1998). A wavelet transform method to
merge Landsat TM and SPOT panchromatic data. International Journal of
Remote Sensing, 19, 743-757.
Zhou, W., Wang, S., Zhou, Y., & Troy, A. (2006). Mapping the concentrations of
total suspended matter in Lake Taihu, China, using Landsat-5 TM
data. International Journal of Remote Sensing, 27, 1177-1191.
76
Table 3-1. Summary of studies on the spectroscopic determination of leaf water content with a focus on LWCD and LWCF. The
references are indexed by the year of publication and summarized with the species examined, the spectral range of the reflectance
data, the analytical method, the expression of leaf water content, and the best result within each study. Note that the studies not related
to LWCD and LWCF but only related to EWT are beyond the scope of this research and not listed.
Reference Species Spectral
range (nm) Method Related to Best accuracy
Curran et al.,
1992
Amaranthus tricolor 400-2400 First derivative spectra LWCD (22.31-91.43 %)
R2 = 0.45,
RMSE = 15.9%
Pe uelas et
al., 1997
5 species (from field)
8 species (potted
seedlings)
390-1100
Spectral index WI
LWCD
LWCD
R2 = 0.31
R2 = 0.49
Dawson et
al., 1998
Pinus elliottii 400-2500 Artificial Netural Network LWCD (52-63 %)
R2 = 0.86,
RMSE = 1.3%
Datt, B.,
1999
21 Eucalyptus species
400-2500
Spectral indices MSI, WI,
(R850 – R2218)/(R850 – R1928);
(R850 – R1788)/(R850 – R1928);
NDWI and TM5/TM7
EWT (0.009-0.025 g/cm2)
LWCF (40.8-71.7 %)
LWCD (70.4-221.5 %)
R2 = 0.61
Not significant
Not significant
Tian et al.,
2001
winter wheat 350-2500 CR over 1650-1850 nm LWCF (39.62-80.12 %)
R2 = 0.87
Pu et al.,
2003
Quercus agrifolia 350-2500 CR centered at 975 nm,
1200 nm and 1750 nm;
three-band ratio indices
derived at 975 nm and 1200
nm
LWCF (0.45-57.94 %)
R2 = 0.86
Maki et al.,
2004
Nerium oleander var.
indicum, Liriodendron
tulipifera, Betula
platyphylla
400-2400
Spectral index: NDWI
EWT (0.002-0.138 g/cm2)
LWCD (33.33-285.71 %)
R2 = 0.62
R2 = 0.08
77
Continued to Table 3-1
Reference Species Spectral
range (nm) Method Related to Best accuracy
Danson &
Bowyer,
2004
subset of LOPEX
Simulations with
PROSPECT model
400-2500
400-2500
Spectral indices MSI, WI,
NDWI, TM5/TM7 and
GVMI
EWT (0.0003-0.0655 g/cm2)
LWCD (9-1258 %)
EWT (0.0425 ± 0.0142 g/cm2)
LWCD (184 ± 101%)
R2 = 0.88, N.L.
R2 = 0.54, N.L.
R2 = 0.88, N.L.
R2 = 0.78, N.L.
Riaño et al.,
2005
37 species from
LOPEX
400-2500 PROSPECT model inversion EWT
LWCD
R2 = 0.94
R2 = 0.33
Stimson et
al., 2005
Pinus edulis
Juniperus
monosperma
350-2300
CR based absorption indices
at 970 nm and 1200 nm; red
edge; spectral indices NDWI
and NDVI
LWCD (approx. 30-60 %)
LWCD (approx. 35-45 %)
R2 = 0.71
R2 = 0.50
Li et al.,
2007
37 species from
LOPEX
400-2500
Genetic Algorithm Partial
Least Squares (GA-PLS)
EWT
LWCD
R2 = 0.94, RMSE
= 0.0017 g/cm2
R2 = 0.89,
RMSE = 68.5%
Colombo et
al., 2008
poplar trees
350-1800
Spectral indices WI, NDWI,
SRWI, NDII, MSI, SR,
(R895 – R675)/(R895 + R675)
PROSPECT model inversion
EWT (0.0091-0.0154 g/cm2)
LWCD (110.65-217.64 %)
EWT (0.0091-0.0154 g/cm2)
LWCD (110.65-217.64 %)
R2 = 0.52
R2 = 0.25
R2 = 0.65
R2 = 0.00
Asner &
Martin, 2008
162 tropical forest
species
400-2500 PLS regression LWCF (43-79 %) R2 = 0.69,
RMSE = 4%
CR: continuum removal; REIP: red edge inflection point
WI = R900/R970; MSI = R1600/R820; NDWI = (R860 - R1240)/(R860 + R1240); GVMI = ((NIR + 0.1) – (SWIR + 0.02))/((NIR + 0.1) + (SWIR + 0.02))
NDVI = (R860 - R690)/(R860 + R690); MDWI = (Rmax1500-1750 - Rmin1500-1750)/(Rmax1500-1750 + Rmin1500-1750), SR = R895/R675, SRWI = R860/R1240
78
Table 3-2. Summary of water content measurements for 265 leaf samples
collected from tropical forests in Panama.
Leaf water content Mean S.D. Minimum Maximum
LWCD (%) 143.60 52.44 32.31 418.20
LWCF (%) 57.23 8.62 24.42 80.70
79
Table 3-3. Spectral indices for predicting vegetation water content
Spectral index Acronym Formula Reference
Water index WI
Peñuelas et al.
(1993, 1997)
Normalized
difference water
index
NDWI
Gao (1996)
Moisture stress
index MSI
Hunt et al. (1987),
Hunt & Rock
(1989)
80
Table 3-4. Coefficients of determination (R2) for correlations between water
content and spectral metrics (wavelet features and spectral indices) derived from
the calibration set (n = 159)
LWCD LWCF
Feature
code
Feature location
R2
Feature location
R2 Wavelength
(nm) Scale
Wavelengt
h (nm) Scale
A
2165 4 0.62*** 2165 4 0.69***
B 1343 7 0.57*** 1344 7 0.62***
C 1869 6 0.51*** 1870 6 0.62***
D
1736 4 0.47*** 1736 4 0.51***
E 2375 4 0.44*** 2378 4 0.51***
F 2034 3 0.44*** 2029 3 0.54***
G 1579 3 0.44*** 1576 3 0.52***
H 2227 3 0.43*** 2226 3 0.54***
I
combo = A,
B, C, D, E,
F, (G, H)
high
& low 0.69***
combo = A,
B, D, E, F,
H, (C, G)
high
& low 0.77***
J
combo = A,
D, F, (E) low 0.67***
combo = A,
D, E, H,
(F)
low
0.76***
K
combo = B,
C high 0.60*** combo = B high 0.62***
L MSI 0.05* MSI 0.08**
M NDWI 0.09*** NDWI 0.12***
N WI 0.09*** WI 0.10***
LWCD: leaf water content by dry mass; LWCF: leaf water content by fresh mass. Scales
were divided into two groups: high (6 and 7) and low (3 and 4). The features in brackets
(e.g. G & H in I) were not included in the feature combination models because they were
rejected during the stepwise regression procedure. Significance is: *p<0.005,
**p<0.0005, ***p<0.0001.
81
Table 3-5. Wavelet features related to major absorptions of particular leaf
biochemical constituents and obtained for LWCD using the calibration set
Feature Related to
(2165, 4) Protein @2172 nm
(1343, 7) Water @ 1400 nm
(1869, 6) Water @ 1940 nm
(1736, 4) Lignin, cellulose @ 1730 nm
(2375, 4) Cellulose, protein @ 2350 nm
(2034, 3) Protein @ 2054 nm
(1579, 3) Not attributable
(2227, 3) Not attributable
* Information on wavelengths of absorption features is from Curran (1989), Kokaly
(2001) and Kokaly & Clark (1999).
82
Table 3-6. Coefficient of determination (R2) and RMSE values comparing the measured water content with that estimated from the
predictive models applied to the validation set (n = 106).
LWCD LWCF
LWCD inverted
from LWCF
Feature code Feature location Accuracy Feature location Accuracy Accuracy
WL (nm) Scale R2 RMSE (%) WL (nm) Scale R
2 RMSE (%) R
2 RMSE (%)
A 2165 4 0.66 28.34 2165 4 0.68 4.86 0.70 26.53
B 1343 7 0.60 30.69 1344 7 0.62 5.28 0.64 29.26
C 1869 6 0.55 32.62 1870 6 0.64 5.20 0.60 30.79
D 1736 4 0.48 35.22 1736 4 0.50 6.07 0.52 33.60
E 2375 4 0.44 36.51 2378 4 0.47 6.27 0.43 36.88
F 2034 3 0.45 36.06 2029 3 0.50 6.09 0.47 35.56
G 1579 3 0.46 35.91 1576 3 0.51 6.02 0.45 36.02
H 2227 3 0.44 36.45 2226 3 0.51 6.05 0.43 36.74
I
combo =
A, B, C,
D, E, F
high
&
low 0.71 26.04
combo =
A, B, D, E,
F, H
high
&
low 0.75 4.34
0.78
23.04
J
combo =
A, D, F low 0.69 26.91
combo =
A, D, E, H
low 0.73 4.47
0.76
23.91
K
combo =
B, C high 0.64 29.30
combo =
B high 0.62 5.28
0.64
29.26
83
Fig. 3-1. Schematic representation of the feature extraction method using
continuous wavelet analysis. Input data sets include the water content and
reflectance measurements of leaf samples. Output is a list of wavelet features
extracted for the estimation of leaf water content.
84
Fig. 3-2. Feature regions extracted from the correlation scalograms relating
wavelet power with water content expressed on the basis of (A) dry mass (LWCD)
and (B) fresh mass (LWCF) in the calibration dataset (n = 159).
85
Fig. 3-3. Example spectra illustrating the effect of different amounts of LWCD on
the reflectance response. Note the change in the amplitude of reflectance in the
1300–2500 nm region and the variations in depth and shape of the absorption
features in the wavelength regions 1670–1830 nm and 2000–2200 nm (denoted by
the horizontal bars) as LWCD changes from the minimum (32.31%) to the
maximum (418.18%) value.
86
Fig. 3-4. Relationships between water content and spectral indices calculated from
the calibration set. Rows represent the same spectral indices. The left column is
for LWCD and the right column for LWCF. All relationships are statistically
significant (p<0.005).
87
Fig. 3-5. Wavelength location of wavelet features indicated by vertical lines and
the corresponding wavelets. The two reflectance spectra are associated with
highest (top) and lowest (bottom) LWCD. Each wavelet feature is positioned on
the spectra with the scaled and shifted continuous wavelet used to compute the
wavelet power. The three numbers beside each vertical line are wavelengths of
start, center and end points of the wavelet. The two dashed vertical lines denote
two features which are removed during the stepwise multiple regression
procedure.
88
Fig. 3-6. Relationships between the wavelet power at (2165 nm, 4) and water
content (A) LWCD and (B) LWCF established with the calibration data set
(p<0.0001). The solid lines are for the entire data set and the dashed line in (A) is
for a subset excluding observations of LWCD above 250%.
89
Fig. 3-7. (A) and (B) are plots of measured versus predicted water contents LWCD
using wavelet feature (2165, 4) and a combination of six features (I, Table 3-6),
respectively. (C) and (D) are plots of measured versus predicted LWCF using
wavelet feature (2165 nm, 4) and a combination of six features, respectively. The
predictive R2 and RMSE values shown are obtained for the validation set. Dashed
lines are 1:1 lines.
90
Fig. 3-8. Inter-relationships between wavelet power, LWCD, and LWCF.
91
Fig. 3-9. Measured versus predicted LWCD transformed from LWCF estimates
presented in Fig. 3-7 C and D. Note the differences as compared to the upper plots
in Fig. 3-7.
92
CHAPTER 4 – EVALUATION OF THE PROSPECT MODEL
AND CONTINUOUS WAVELET ANALYSIS FOR EFFICIENT
ESTIMATION OF LEAF WATER CONTENT4
4.1. Introduction
Over the last two decades, laboratory and imaging spectroscopy data have
been extensively used to estimate chemical constituents (e.g., chlorophyll, water,
nitrogen) in vegetation in response to the need for information on vegetation
chemistry (Asner & Vitousek, 2005; Curran et al., 2001; Kokaly & Clark, 1999;
Peterson et al., 1988; Smith et al., 2002). In particular, the accurate retrieval of
vegetation water content is crucial to the assessment of plant physiological status
Pe uelas et al., 1997; Pu et al., 2004; Stimson et al., 2005), to the determination
of wildfire risk (Chuvieco et al., 2002; Dennision & Moritz, 2009; Dennison et
al., 2008; Maki et al., 2004; Yebra et al., 2008) and as a critical leaf trait in
ecological applications (Asner & Martin, 2008; Garnier & Laurent, 1994;
Sánchez-Azofeifa et al., 2009).
A common measure of water content in leaves is the leaf gravimetric
water content (GWC) which is defined as the amount of water as a percentage of
dry mass or fresh mass (Datt, 1999). The detection of leaf GWC in the optical
domain has been estimated based on the relationship between the reflectance at
the 700-2500 nm and the abundance of water (Carter, 1991; Tucker, 1980). Many
studies suggest that it is difficult to derive accurate estimates of GWC from leaf
reflectance, particularly for a variety of species (Colombo et al., 2008; Danson &
Bowyer, 2004; Datt, 1999; Li et al., 2007; Maki et al., 2004; Riaño et al., 2005).
Some studies have established strong relationships between leaf GWC and
spectral indices that are designed to capture the spectral variation in water
absorption features centered near 970 nm 1200 nm and 1450 nm Danson
4 Thanks to Stéphane Jacquemoud, Jean-Baptiste Feret, and Christophe Francois for
making the version 4 of the PROSPECT model available online
(http://teledetection.ipgp.jussieu.fr/prosail/).
93
owyer 2004; Pe uelas et al., 1997). Changes in leaf GWC may also be related
to variations in reflectance associated with dry matter absorption features that are
clearly discernable in the reflectance spectra of dry plants but obscured due to the
presence of leaf water. Ceccato et al. (2001) have shown that leaves with different
values of GWC are likely to have different amounts of dry mass (i.e., dry matter
content) that directly affects the spectral reflectance in the shortwave infrared
(SWIR) region. Tian et al. (2001) provided the only study that paid particular
attention to the absorption features of dry matter in the 1650-1850 nm range in
relation to leaf GWC. However, there has been no assessment of the relative
merits of dry matter and water absorption features over the entire SWIR region
for the purpose of leaf GWC estimation.
Continuous wavelet analysis (CWA) is an emerging spectral analysis tool
for decomposing leaf reflectance spectra into a number of scale components.
CWA provides an effective way to examine all absorption features in leaf
reflectance at various scales (Blackburn & Ferwerda, 2008). The use of CWA also
makes it possible to extract wavelet features (coefficients) that capture useful
spectral information pertinent to leaf water (Cheng et al., 2010). In Chapter three,
CWA was applied to measured leaf reflectance spectra from a collection of
tropical forest species and models for the prediction of leaf GWC were presented.
Using this methodology, a number of wavelet features were extracted from leaf
reflectance spectra and used to derive accurate estimates of leaf GWC. In this
study, I conduct a comparative assessment of the CWA method when applied to a
leaf spectral database simulated with the PROSPECT leaf radiative transfer
model.
The radiative transfer model PROSPECT has been successfully used to
design or evaluate vegetation indices (Ceccato et al., 2002; Haboudane et al.,
2002) and develop inversion approaches (Demarez et al., 1999; Jacquemoud et
al., 1996; Zarco-Tejada et al., 2003), to retrieve vegetation properties from
remotely sensed reflectance. The principal aim of this study is to evaluate the
performance of the wavelet-based methodology for the estimation of leaf GWC
using spectra simulated with PROSPECT and to determine whether the wavelet
94
features derived from the simulated spectra are consistent with those obtained in
Chapter three from the measured spectra. A secondary objective of this study is to
assess the ability of the PROSPECT model to simulate leaf reflectance for a range
of Mesoamerican tropical forest species. Few studies have evaluated the
performance of PROSPECT against experimental data (Feret et al., 2008;
Jacquemoud et al., 1996; Jacquemoud et al., 2000; le Maire et al., 2004).
4.2. Materials and methods
4.2.1. Description of leaf reflectance and mass measurements
Leaf samples were collected from two tropical forest sites in the Republic
of Panama. The first site is located in the dry forest of Parque Natural
Metropolitano (PNM) near the Pacific coast and the second site in the wet forest
of Fort Sherman (FS) on the Caribbean coast. The PNM forest experiences a
severe dry season from mid-December to the end of April and has an annual
rainfall of about 1,740 mm. The FS forest experiences a mild dry season from
January to March and has an annual rainfall of about 3300 mm. Construction
cranes owned by the Smithsonian Tropical Research Institute (STRI) at both sites
allow flexible access to the top of the canopy and convenient collection of leaf
samples (Castro-Esau et al. 2004).
In March 2007, 265 leaf samples were collected from twenty-three species
of lianas and eight species of trees at PNM and from eight species of lianas and
eight species of trees at FS. All samples consisted of sun leaves. Protocols for leaf
clipping and handling presented in Sánchez-Azofeifa et al. (2009) were followed
to prepare for reflectance and leaf mass measurements. The reflectance of leaves
was recorded from 350 to 2500 nm with a FieldSpec®
FR spectroradiometer
(ASD Inc., Boulder, CO, USA) that provides a spectral resolution of 3 nm at 700
nm, 10 nm at 1500 nm and 10 nm at 2100 nm. Three reflectance measurements
were taken per leaf with an ASD leaf clip covering a halogen bulb illuminated
area with a radius totaling 10 mm. The mean of the three reflectance
measurements provided a representative reflectance spectrum for each leaf. Five
95
or ten leaf samples were measured per species. For each leaf, the wet weight was
determined within one hour after clipping and the dry weight was obtained from
the sample after a three-day drying process at 60oC. Leaf water content was then
estimated using the wet weight and the dry weight.
4.2.2. Simulation of leaf reflectance with the PROSPECT model
4.2.2.1. Principle of the PROSPECT model
PROSPECT is a radiative transfer model that describes the leaf optical
properties from 400 nm to 2500 nm (Jacquemoud & Baret, 1990). With a new
version of the model (PROSPECT-4, Feret et al., 2008), leaf reflectance spectra
can be simulated at 1nm steps with four input parameters: leaf structure N, leaf
chlorophyll a+b concentration (Ca+b), equivalent water thickness (Cw), and dry
matter content (Cm). All parameters can be measured from leaves except N. The
model considers a leaf to consist of N stacked elementary homogeneous layers
that account for leaf internal scattering and absorption by specific biochemical
constituents. Therefore, N affects the reflectance in the entire spectral range with a
dominant influence in the near-infrared (NIR) region. Ca+b mainly controls
spectral variation in the visible and NIR regions, while Cw coupled with Cm
affects the reflectance in the NIR and SWIR regions. As described below,
chlorophyll concentration was kept constant for the simulations of this study. As a
physically based model, PROSPECT is commonly used to represent leaf optical
properties for specific ecosystems based on a range of parameter values that are
site specific (Danson & Bowyer, 2004; Yebra et al., 2008; Yebra & Chuvieco,
2009).
4.2.2.2. Parameterization for the simulations
Simulations of leaf reflectance spectra were conducted as part of two
experiments. In the first experiment, the simulation of reflectance for each leaf
sample was optimized to match the measured reflectance spectrum.
Measurements of Cw and Cm for each leaf were used to optimize N during
simulations. From this experiment, I estimated the range of N values necessary to
96
simulate all spectral measurements and assessed the performance of PROSPECT
to simulate the reflectance measurements from tropical leaves. In the second
experiment, leaf reflectance spectra were simulated for a range of input
parameters and used to test the wavelet-based method for the estimation of leaf
GWC.
Experiment I: simulation of the measured leaf reflectance
The first experiment aimed to simulate the measured reflectance from 800
to 2500 nm (n=265). To constrain the simulation, Cw and Cm were obtained from
the measured leaves and Ca+b was kept at a constant value of 33 µg/cm2 (Ceccato
et al., 2001). For each observation, a number of simulations were conducted by
varying N from a value of 1 to 4 at increments of 0.1. The optimal N value for
each leaf was taken as the value that minimized the Euclidean distance between
the measured spectrum and the simulated spectrum. The N values determined in
this experiment were then used to constrain the range of N values utilized in the
second experiment. The overall ability of PROSPECT to model the observed leaf
reflectance was evaluated using the root mean square error (RMSE) per
wavelength defined as follows:
(4-1)
where and
are the measured and simulated reflectance
values at wavelength λ for sample i, respectively.
Experiment II: simulation of leaf spectra for the estimation of leaf GWC
In the second experiment, a total of 530 simulations were conducted using
a combination of input values for each of the four PROSPECT parameters. The
outcome was a spectral database twice as large as that of the measured spectra
(n=265). The simulated spectral database was divided into two portions, with 60%
of the data being used to develop predictive models for the estimation of leaf
GWC and 40% to validate the predictive models. For each simulation Ca+b was
kept at a constant value of 33 µg/cm2 and N, Cw and Cm were randomly selected
97
from uniform distributions within specific data ranges. The measured ranges of
Cw and Cm values were used and the range of N value was set to that obtained in
Experiment I. A summary of all parameters is provided in Table 4-1. For each
simulation, GWC was computed as follows on the basis of dry weight (LWCD)
and fresh weight (LWCF):
(4-2)
(4-3)
In Chapter three I was able to obtain more accurate estimates of LWCF than
LWCD. Estimates of LWCD can be determined from estimates of LWCF using the
following equation:
(4-4)
A summary of the LWCF values measured for the 265 leaf samples and calculated
for the 530 simulated leaf reflectance spectra is shown in Fig. 4-1.
4.2.3. Feature extraction from wavelet analysis to estimate leaf GWC
4.2.3.1. Wavelet analysis
Wavelet analysis is a useful mathematical tool that provides a way to
analyze spectral signatures at various scales by decomposing the original data into
multiple scale components (Bruce et al., 2001; Kaewpijit et al., 2003; Mallat,
1989; Rivard et al., 2008). In particular, wavelet analysis of hyperspectral data has
proven to be effective for a variety of vegetation studies such as forest species
identification (Kalácska et al., 2007; Zhang et al., 2006), biochemical/biophysical
parameter estimation (Blackburn, 2007; Blackburn & Ferwerda, 2008; Ferwerda
& Jones, 2006; Pu & Gong, 2004) and stress detection (Cheng et al., 2010).
Wavelet transforms include the discrete wavelet transform (DWT) and the
continuous wavelet transform (CWT) (Blackburn & Ferwerda, 2008; Bruce et al.,
2001). The latter is adopted in this study because each scale component is directly
comparable to the input reflectance spectrum (Bruce et al., 2001; Du et al., 2006).
In addition, CWT is able to provide valuable information pertinent to the shape
98
and position of spectral features in leaf reflectance spectra (Blackburn &
Ferwerda, 2008).
4.2.3.2. Continuous wavelet transform (CWT)
The CWT is a linear operation that uses a mother wavelet function ψa,b(λ)
to convert a reflectance spectrum f(λ) into sets of coefficients based on the
following equation (Mallat, 1991):
(4-5)
where is the complex conjugate of
5 . a and b are positive real
numbers with the scaling factor a defining the width of a continuous wavelet and
the shifting factor b defining the position. The magnitude of a wavelet coefficient,
also referred to as wavelet power, denotes the correlation between a scaled and
shifted version of the mother wavelet and a spectral segment of the input
spectrum. The scale components are of the same length and are suited to
characterize absorption features of various widths.
In order to detect the absorption features attributable to leaf water and dry
matter, the second derivative of Gaussian (DOG), also known as the Mexican Hat,
was used as the mother wavelet basis (Torrence & Compo, 1998; Cheng et al.,
2010). The effective support range of the Mexican Hat is [-5, 5] for the scale a=1
and [-5a1, 5a1] for a=a1 (Du et al., 2006). The width of a scaled wavelet (10a1)
determines the number of input wavebands that are to be convolved with the
wavelet and attributed to the wavelet coefficient. To reduce the data volume, the
CWT was performed at dyadic scales 21, 2
2, 2
3, ..., and 2
8. Those scales were
labeled as scales 1 2 3 … and 8 and were comparable to the scales described in
relevant studies by Blackburn & Ferwerda (2008) and Rivard et al. (2008). For
the PROSPECT-simulated reflectance spectra, 1701 wavebands were available
(800-2500 nm). Any scale greater than 28=256 was discarded as they were not
observed to carry meaningful spectral information (Cheng et al., 2010). All CWT
5 Note that complex conjugation changes the function only if a complex wavelet function such as
Morlet function is used. The derivatives of Gaussian function are real functions.
99
operations were conducted using the IDL 6.3 Wavelet Toolkit (ITT Visual
Information Solutions, Boulder, CO, USA).
4.2.3.3. Feature selection from correlation scalograms
Four procedural steps were involved to define spectral features that
significantly correlated with LWCF. A brief description of the procedure is
provided in this section and readers are referred to Chapter three for further detail.
Firstly, CWT was applied to each of the reflectance spectra simulated in
Experiment II to generate a wavelet power scalogram representing the wavelet
power as a function of wavelength and scale. Secondly, a correlation scalogram
was constructed by establishing the Pearson’s correlation for each element of the
wavelet power scalograms and LWCF across all simulations. The correlation
scalogram formed a feature set from which wavelet features most sensitive to
LWCF could be selected. Thirdly, features with the least statistically significant
R2 (p>=0.05) values were discounted. The remaining features were sorted in
descending order of R2 and a R
2 cut-off value was applied to retain the 1%
features that most strongly correlated to LWCF. This process delineated a number
of feature regions on the correlation scalogram. As a last step, the feature with the
maximum R2 within each feature region was selected and expressed as
(wavelength in nm, scale). This feature selection approach resulted in a small
number of wavelet features that were sparsely distributed on the correlation
scalogram and capable of capturing the most important information with respect
to changes in LWCF.
4.2.4. Calculation of spectral indices
The wavelet-based method was compared to three spectral indices
reported in the literature and designed to estimate vegetation water content from
remotely sensed reflectance were calculated. The water index (WI), originally
developed to relate LWCD with leaf reflectance in narrow wavebands, is
formulated as follows (Peñuelas et al., 1993, 1997):
100
(4-6)
The moisture stress index (MSI) was developed using Landsat TM bands TM4
and TM5 (Hunt et al., 1987) and tested with high spectral resolution data. MSI
was calculated using the following equation (Hunt & Rock, 1989):
(4-7)
The normalized difference water index (NDWI) was designed by Gao (1996) to
remotely sense the EWT from space and was originally formulated using two
narrow wavebands from MODIS imagery as follows:
(4-8).
4.3. Results
4.3.1. Experiment I: simulation of the measured leaf reflectance
Fig. 4-2A shows a summary of leaf reflectance for measured and
simulated spectra. The shape of the mean reflectance spectra and deviations to the
mean for the two data sets is similar in the entire spectral range with exception for
the 800-900 nm region. For the 900 to 2500 nm region, of interest for estimating
leaf water content, the spectral RMSE was less than 0.03, indicating a very good
agreement between the simulated and measured leaf reflectance spectra (Feret et
al., 2008; Jacquemoud et al., 1996; Jacquemoud et al., 2000) (Fig. 4-2B).
Specifically, the globally lowest RMSE of 0.006 was observed at 1370 nm
on the leading edge (1310-1386 nm) of a broad water absorption region where
PROSPECT performed best. Two other spectral regions at 1660-1780 nm and
2130-2230 nm displayed locally low values in RMSE (RMSE1702 = 0.009,
RMSE2159 = 0.020). These two regions denote absorption by dry matter. The
following section shows that the three spectral regions carry considerable spectral
information sensitive to changes in LWCF.
101
4.3.2. Experiment II: simulation of leaf spectra for the estimation of
leaf GWC
4.3.2.1. Feature regions determined from the correlation scalogram
Six feature regions that correlate with leaf water content were determined
from the correlation scalogram (Fig. 4-3). All feature regions were located in the
SWIR region (1300-2500 nm) and the largest extended from 1692 nm to 1748 nm
across scale 3 to 5. The spatial pattern of the feature regions was highly uneven,
with the largest region encompassing 81.36% of the features (96 of 118 features)
and the remaining five regions encompassing 18.64%.
4.3.2.2. Wavelet features most strongly correlated to LWCF
Six wavelet features (one per feature region) were identified and shown to
be strongly sensitive to LWCF (Table 4-2). The R2 value of the linear regression
for each feature was high (R2 from 0.989 to 0.975). The difference in R
2 between
the strongest (feature A) and weakest feature (feature F) was only 0.014. All
features except feature F (scale 7) are observed in low scales (scales 3 and 4).
Feature D (1802 nm) is spectrally redundant with feature C (1800 nm) given the
spectral uncertainties of the spectrometer used in the SWIR region.
Fig. 4-4A displays the wavelength and scale of the five distinct wavelet
features. These are shown with reflectance spectra for the lowest (16.80%) and
highest LWCF (85.57%). The low-scale features occurred in two spectral regions
where leaf dry matter (e.g., protein, lignin, cellulose) constituents produce broad
and overlapping absorption features (Curran, 1989). In response to changes in
LWCF, four of the low-scale features captured spectral variation in the 1660-1820
nm range that is primarily influenced by the presence of lignin and cellulose in
plants (Table 4-2). Feature E captured the spectral variation in the 2140-2220 nm
range attributed to the presence of protein, lignin, and cellulose (Curran, 1989;
Kokaly, 2001). Feature F (1337 nm, 7) occurred on the edge of a broad water
absorption and was attributed to broader changes in the shape of reflectance
spectra affected by changes in LWCF.
102
4.3.2.3. Relative performance of wavelet features and spectral indices
Fig. 4-5 shows the regression model for the best performing wavelet
feature (1740nm, 4) and the comparison between measured and predicted LWCF
values derived from the model. The relationship between measured LWCF and
wavelet power at this feature is strongly linear. Similarly strong linear
relationships were observed for all features in Table 4-2.
When the regression model for each feature is applied to the validation set
for the prediction of LWCF, the ranking of R2 for the six feature (Table 4-3) is
almost the same as that obtained for the calibration set (Table 4-2). The accuracy
for the estimation of LWCF based on the six wavelet features ranged from RMSE
values of 1.58% (R2 = 0.988) to 2.37% (R
2 = 0.974) (Table 4-3). A model based
on the combination of the five low-scale features predicted LWCF with the same
accuracy as the combination of all features (R2 = 0.990, RMSE = 1.46%), whereas
the model based on the high-scale feature resulted in a lower accuracy (R2 =
0.974, RMSE = 2.37%). These accuracy values are higher than those reported in
the literature (Asner & Martin, 2008). Fig. 4-6 compares the actual LWCF for
simulated spectra with LWCF predicted using the combination of all features and
the data were distributed more uniformly around the 1:1 line than that observed
using the best performing individual feature (Fig. 4-5).
All three spectral indices yielded significantly less accurate estimates of
LWCF than wavelet features with the WI being the best performing index (Table
4-3). The calibration model obtained for WI displays a weaker correlation (R2 =
0.575) (Fig. 4-7A) compared to that obtained for the best wavelet feature (Fig. 4-
5A). Using WI, LWCF values of less than 35% appeared to be substantially
overestimated (Fig. 4-7B) and the RMSE of the prediction was 7.65% higher than
that for feature (1740 nm, 4) (RMSE=1.58%).
4.3.2.4. Transformation of LWCF to LWCD
To facilitate comparison with previous studies on LWCD, LWCF estimates
were transformed to LWCD using Eq. (4-4). For this purpose I used LWCF
predicted with the best performing wavelet feature (1740nm, 4) and the
103
combination of six wavelet features (Table 4-3). The accuracy of LWCD
estimated using feature (1740nm, 4) (Fig. 4-8A, R2 = 0.933, RMSE = 25.07%)
and the combination of the six features (Fig. 4-8B, R2 = 0.950, RMSE = 21.70%)
were higher than that reported for PROSPECT simulated spectra (Danson &
Bowyer, 2004) and LOPEX data (Danson & Bowyer, 2004; Li et al., 2007; Riaño
et al., 2005). The LWCD estimates compare well with the actual values at low
values but the comparison degrades with increasing values of LWCD (Fig. 4-8).
Such a pattern was not observed for predicted LWCF (Figs. 4-5, 4-6).
4.4. Discussion
This study introduces a wavelet-based methodology applied to simulated
reflectance spectra to achieve accurate estimates of both measures of leaf GWC
(LWCF or LWCD). This method is effective to extract spectral information
indicative of changes in leaf GWC and differs from that reported in related studies
(Asner & Martin, 2008; Danson & Bowyer, 2004; Tian et al., 2001).
4.4.1. Advantages of the continuous wavelet analysis
As a response to changes in a leaf chemical, significant spectral variation
tends to occur over particular absorption regions rather than at scattered
individual wavelengths. The use of CWA provides a multiscale representation of
input reflectance information and facilitates the analysis of all absorption features
of various widths. The wavelet features are especially important for capturing
variations in the shape of relevant spectral regions. Furthermore, the selection of
optimal features from the entire correlation scalogram ensures that the significant
spectral variation is captured regardless of its width and wavelength locations. In
contrast, spectral indices simply use a small number of wavebands to characterize
the leaf water-induced spectral variation over a broad range, which explains their
poorer performance.
Empirical relationships between leaf GWC and the reflectance at water
absorption bands have been employed to estimate leaf GWC Danson owyer
104
2004; Pe uelas et al., 1997). For this purpose, little attention has been paid to date
to the use of spectral regions recording light absorption by dry matter. Tian et al.,
(2001) examined the 1650-1850 nm dry matter absorption feature and found a
strong relationship between continuum-removed reflectance spectra and GWC.
The wavelet-based method of this study exploited a number of absorption features
of dry matter in the SWIR region, thereby emphasizing the important role of dry
matter features in estimating GWC.
4.4.2. Comparison of wavelet features derived from the simulated
spectra and the measured spectra
To compare the performance of the wavelet-based methodology across
data sets, the procedures presented in Section 4.2.3 were also applied to the
measured reflectance data set. The wavelet features derived are displayed in Fig.
4-4B and their predictive capabilities are summarized in Table 4-4. The
PROSPECT-simulated spectra resulted in a smaller number of informative
wavelet features that showed stronger capabilities to predict leaf GWC (Tables 4-
3 & 4-4). Six significant features were extracted from the simulated spectra and
eight were extracted from the measured spectra. The smaller number of features
for the simulated spectra might be explained by a large feature region (Fig. 4-3)
that accounted for a large portion of the top 1% features in the correlation
scalogram.
Three features ((1740nm, 4), (2180nm, 3), (1337nm, 7)) determined from
the simulated spectra were closely matched by features from the measured spectra
((1736nm, 4), (2165nm, 4), (1344nm, 7)). Interestingly, these similar wavelet
features occurred in spectral regions where the simulated leaf reflectance was in
good agreement with the measured reflectance (Fig. 4-2). Differences in the
location of the remaining features between the two data sets cannot be explained
at this time but may be related to the relatively lower accuracy of simulation in
the remaining spectral regions.
105
4.4.3. Distribution of spectral information across scales
The most apparent spectral change for dehydrating leaves is the increase
in reflectance throughout the 400-2500 nm range, with the most prominent
increase occurring in the SWIR region (1300-2500 nm) (Aldakheel & Danson,
1997; Carter, 1991, Lee et al., 2007). Thus one might expect that changes in leaf
GWC might be best captured by high-scale wavelet features in response to
changes over broad spectral regions. However, the relative importance of high-
scale features among all features for each data set was significantly different.
Among the eight features derived from the measured spectra, two high-scale
features ((1344nm, 7) & (1870nm, 6)) showed relatively strong correlations with
leaf GWC, ranking immediately below the feature with the strongest correlation.
This feature distribution across scales for the measured spectra is not unexpected.
For the simulated spectra, the high-scale feature (1337nm, 7) provided the
weakest correlation amongst the six features, which is unexpected.
The unexpectedly least important high-scale feature for the simulated data
set might be explained by the difficulty in parameterizing the PROSPECT model
in an appropriate way. The PROSPECT model provides a user with control of
four input variables but random selections of each variable value can lead to
unrealistic input combinations (Yebra & Chuvieco, 2009). N affects the spectral
variation throughout the 800-2500 nm range, and it impacts variations in
reflectance amplitude as GWC does (i.e., Cw and Cm) (Fig. 4-9). Usually, a leaf
with low GWC would be accompanied by a high value of structural parameter N
giving a reasonably high reflectance. Through random combinations of input
variables, a low GWC value (derived from Cw and Cm) can be assigned to any N
in the defined range, resulting in an unrealistic combination. Fig. 4-10 illustrates
some problematic spectra generated by unrealistic combinations of input
variables. As LWCF decreased from 83.65% to 67.47% (top to bottom in Fig. 4-
10), the leaf reflectance should have increased in the infrared region but decreased
due to the considerable influence of N. In our simulation I did not fix N as doing
so would have failed to represent leaf structural variations present in measured
spectra. A large number of such problematic spectra resulting from unrealistic
106
parameter combinations might confound the link between GWC and spectral
reflectance. At the very least, they may prevent high-scale wavelet features from
capturing significant information on amplitude variation over a broad spectral
region.
To reduce the risk of generating a large number of problematic spectra,
further efforts could eliminate the simulations resulting from unrealistic
combinations of N, Cw and Cm by applying a filter criterion based on the empirical
relationships between input variables (Yebra et al., 2008). Alternatively, some
conditions could be applied to constrain the combination of input parameters prior
to simulation. Previous studies have kept all variables independent because no
accurate information on the relationship between variables was available for a
specific geographic site. To avoid the presence of site-specific information in the
model, future versions of PROSPECT may need to incorporate more input
variables to account for the interacting effect between the current variables.
This study suggests that the wavelet features derived for the estimation of
leaf GWC are not sensitive to variability in N that represents the leaf structural
variation for a wide range of tropical forest species. With the use of the wavelet-
based methodology, the influence of variation in leaf structure was implicitly
suppressed but never explicitly removed. This suppression is beneficial in tropical
ecosystem studies for reducing the spectral variability that often changes
significantly with species diversity (Castro-Esau et al., 2006).
4.5. Conclusions
The PROSPECT model was able to well represent the reflectance of
leaves collected from Mesoamerican tropical forest environments and performed
best while reconstructing the reflectance in three local regions (1310-1386 nm,
1660-1780 nm, and 2130-2230 nm). Using the wavelet-based method, six
significant wavelet features were determined from the PROSPECT-simulated
spectra and all were able to produce accurate estimates of leaf GWC. Three of
107
these features closely matched those obtained in Chapter three for the measured
spectra. These recurrent features occurred in spectral regions where the leaf
reflectance was best modeled by PROSPECT. It appears that these features may
serve as robust and efficient predictors of leaf GWC for a broad variety of tropical
forest species. Results from both the simulated spectra and measured spectra
showed that low-scale features were reliable for the estimation of leaf water
content but observations regarding the importance of high-scale features remain
inconclusive.
This research provided a valuable opportunity to assess the ability of
PROSPECT to simulate the spectral reflectance of Mesoamerican tropical forest
species with particular considerations paid to their link to leaf water content. It
also demonstrated the robustness of the wavelet-based methodology to extract
meaningful spectral features in the wavelet domain through a modeling approach.
The three wavelet features consistently determined from the simulated spectra and
the measured spectra are thereby recommended to the reflectance spectroscopy
community for efficient estimation of GWC at least as a supplement to spectral
indices. If one is to design any GWC metric for a specific application without
relation to wavelets, attention to the spectral regions covered by the wavelet
features of this study is recommended.
108
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Table 4-1. Ranges of input variables used for the PROSPECT simulations in
Experiment II
Input parameter Unit Range
Chlorophyll µg/cm2 33
Equivalent water content (EWT) cm or g/cm2 0.0037-0.0255
Dry matter content (DMC) g/cm2 0.0041-0.0189
Structural parameter N - 1.1-2.9
114
Table 4-2. List of wavelet features ranked by R2 using the calibration set and
relating wavelet power to measured leaf water content
Note: Wavelet features were associated with broad absorptions tabled in Curran
(1989) and Kokaly & Clark (1999).
Feature Wavelength (nm) Scale R2 Attributed to
A 1740 4 0.989 Cellulose, lignin @ 1730 nm
B 1780 3 0.987 Cellulose, sugar @ 1780 nm
C 1800 4 0.984 Not attributable
D 1802 3 0.982 Not attributable
E 2180 3 0.976 Protein, nitrogen @ 2180 nm
F 1337 7 0.975 Water @ 1400 nm
115
Table 4-3. Accuracies for the estimation of LWCF in the validation set using
spectral indices, individual wavelet features or a combination of wavelet features
derived from the simulated spectra.
Feature
code
Feature location Accuracy
Wavelength (nm) Scale R2 RMSE (%)
A 1740 4 0.988 1.58
B 1780 3 0.982 1.94
C 1800 4 0.982 1.96
D 1802 3 0.982 1.95
E 2180 3 0.978 2.18
F 1337 7 0.974 2.37
G Combo = A, B, C, D, E, F High & Low 0.990 1.46
H Combo = A, B, C, D, E Low 0.990 1.46
I Combo = F High 0.974 2.37
J MSI 0.308 12.1
K NDWI 0.495 10.3
L WI 0.599 9.23
116
Table 4-4. Accuracies for the estimation of LWCF in the validation set using
individual wavelet features derived from the measured spectra.
Feature code Feature location Accuracy
Wavelength (nm) Scale R2 RMSE (%)
A 2165 4 0.68 4.86
B 1344 7 0.62 5.28
C 1870 6 0.64 5.20
D 1736 4 0.50 6.07
E 2378 4 0.47 6.27
F 2029 3 0.50 6.09
G 1576 3 0.51 6.02
H 2226 3 0.51 6.05
117
Fig. 4-1. Histograms of leaf water content by fresh weight (LWCF) derived from
(A) the laboratory measurements on each leaf and (B) values of Cw and Cm for the
PROSPECT simulations.
118
Fig. 4-2. (A) Plot of mean and mean ± s.d. of reflectance spectra for the measured
leaf reflectance dataset and the PROSPECT simulated dataset. (B) The root mean
square error (RMSE) per wavelength as described in Eq. (4-1). The dashed circles
highlight spectral regions displaying local minimum in RMSE.
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Fig. 4-3. Features regions extracted from the correlation scalogram relating
wavelet power and leaf water content (LWCF). The feature with strongest
correlation (1740 nm, 4) originates from the largest feature region. Arrows mark
the wavelength position of wavelet features representative of each feature region.
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Fig. 4-4. Wavelet features used for the estimation of LWCF. The wavelength
position and scale of those features are indicated by vertical lines and the
corresponding wavelets. Also shown are reflectance spectra for highest LWCF
(dashed line) and lowest LWCF (dotted line). Each wavelet feature is positioned
on the spectra with the scaled and shifted continuous wavelet used to compute its
wavelet power. (A) Wavelet features derived from the PROSPECT simulated
reflectance spectra. (B) Wavelet features derived from the measured reflectance
spectra.
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Fig. 4-5. (A) Correlation between the best performing wavelet feature (1740 nm,
4) and leaf water content (LWCF) for the calibration set. (B) Estimates of LWCF
derived from the regression model in (A).
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Fig. 4-6. Plot of actual versus predicted LWCF derived using a combination of the
six wavelet features for the simulated spectra.
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Fig. 4-7. (A) Relationship between the water index (WI) and leaf water content
(LWCF) for the calibration set. (B) Estimates of LWCF derived with the
regression model in (A).
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Fig. 4-8. Actual LWCD plotted against predicted LWCD inverted from LWCF
estimates. The LWCF were obtained from wavelet feature (1740 nm, 4) for (A)
and from the combination of all features for (B).
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Fig. 4-9. Effects of leaf properties on the reflectance simulated by the PROSPECT
model: (A) leaf structure, (B) equivalent water thickness, and (C) dry matter
content. Also shown in (D) is the coupled effect of equivalent water thickness and
dry matter content.
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Fig. 4-10. Example PROSPECT-simulated reflectance spectra with randomly
generated combinations of LWCF and N. Note that reflectance spectra simulated
with higher LWCF values should display lower reflectance in the infrared region
but do not as a result of unrealistic combinations of input variables.
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CHAPTER 5 - CONCLUSIONS
5.1. Summary
This research has focused on the development of methodologies to extract
useful spectral information from leaf reflectance spectra using continuous wavelet
analysis (CWA). One methodology has been used for detecting the effect of
mountain pine beetle infestation at the early stage on lodgepole pine trees, and the
other for deriving robust predictors of leaf water content from measured and
simulated reflectance spectra. As presented in the preceding chapters, CWA
provides a novel approach to optimize the selection of wavelet features as a
function of wavelength and scale.
Three research issues were addressed in this thesis. The first issue dealt
with the development of an effective method to detect the green attack stage on
lodegepine trees affected by mountain pine beetles. Through the use of CWA, a
small number of wavelet features were determined to distinguish healthy trees
from infested trees at the green attack stage. Water was found to be a
physiological indicator of the beetle infestation at the early stage, therefore the
second issue focused on the development of a methodology to determine the
universal spectral information that relates to the leaf gravimetric water content
(GWC) for a variety of forest species. In an effort to derive accurate estimates of
leaf GWC, eight meaningful wavelet features were extracted to account for the
spectral variations linked to changes in leaf GWC. To further determine the robust
wavelet features pertinent to leaf water, the third issue addressed a simulation
study to test the newly developed methodology for the estimation of leaf GWC
from the reflectance spectra simulated by the radiative transfer model
PROSPECT.
5.2. Synthesis of contributions
In the context of vegetation studies, previous research involved with
wavelet analysis of hyperspectral data has focused on the exploration of discrete
wavelet transform (DWT) as a means to reduce the dimensionality of
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hyperspectral signatures (Bruce et al., 2001; Koger et al., 2003; Pu & Gong,
2004). I chose continuous wavelet transform (CWT) instead of DWT to
decompose the leaf reflectance spectra because it is easier to interpret the outputs
of CWT and to compare them with the input spectra (Blackburn & Ferwerda,
2008; Rivard et al., 2008). To date, there are very few studies that apply CWA to
hyperspectral signatures of vegetation (Blackburn & Ferwerda, 2008; Ferwerda &
Jones, 2006). This is likely due to the research gap in the development of effective
feature extraction/selection techniques that serve to derive a small number of
useful features from a large volume of CWT outputs. A methodological highlight
of this work lies in the development of a new way to select in the wavelet domain
the most significant features for detecting the green attack damage and for
predicting leaf GWC.
Chapter 2 reports the most promising findings to date on the remote
detection of green attack damage due to mountain pine beetle infestation. The two
relevant studies (Ahern, 1988; Runesson, 1991) focused on the examination of
spectral variations in the visible and near infrared regions (350-1100 nm) and thus
precluded the potential contribution of spectral signatures from water. However,
the reflectance measurements from 350 to 2500 nm are readily available now with
the advancement of the state of the art of reflectance spectrometry. The primary
findings of this study are: 1) The infested trees at the green attack stage suffer
from water deficit. This study presents the first explicit examination of tree-level
water availability related to mountain pine beetle green attack damage, although
White et al. (2007) indicated the water deficiency at the stand level as a
consequence of beetle attack at a later stage (red attack). The finding increases our
understanding of the physiological mechanism of the pre-visual stress from
mountain pine beetle attack. 2) The water deficit occurring in infested trees could
be detected with hyperspectral reflectance measurements of pine needles. Despite
the reported challenge in detecting green attack damage via remote sensing
(Wulder et al., 2006), the use of CWA allows us to capture the spectral response
to the water deficit triggered by the beetle attack on pine trees. It is shown that the
spectral detection of green attack damage should focus on spectral regions where
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the variation in reflectance is strongly associated with changes in foliage water. In
recognition of the importance of water content as an indicator of green attack
damage, the following two chapters focus on examining the spectral contributions
of water and strive to achieve accurate estimates of leaf GWC.
Chapter 3, unlike previous investigations conducted on a limited number
of species or a narrow range of water content levels, is based on a data set
encompassing 47 species from two tropical forest environments (dry forest and
rainforest) in Panama. CWA was shown to be effective to capture the spectral
variations in response to changes in GWC despite the diverse composition of
species. The most interesting finding of this chapter stems from the outcome of
the selection of optimal wavelet features through the use of CWA. Two groups of
features were determined at various scales to be sensitive to changes in leaf GWC.
The first group, found at high scales, captures the amplitude variation across a
broad spectral range that is primarily attributed to changes in the amount of leaf
water. The second group, found at low scales, captures the variations in the shape
and depth of absorption features by dry matter that comprises the dry mass of
leaves such as protein, lignin, and cellulose. Although GWC is dependent on the
absolute amount of leaf water and the dry matter content (Danson & Bowyer,
2004), the results suggest that spectral information pertinent to both leaf water
and dry matter is useful for the spectroscopic estimation of leaf GWC. In addition,
it adds a new dimension to the understanding of the spectral variations induced by
changes in leaf GWC. This study is the first to use a species-rich data set collected
from the Mesoamerican tropical ecosystem to address the estimation of leaf
chemistry. The most similar published study was conducted by Asner & Martin
(2008) who used a Partial Least Squares (PLS) method to investigate the
estimation of leaf chemistry for 162 Australian tropical forest species. Compared
with CWA, PLS requires more effort to calibrate models and does not provide
determinant information to interpret the relative importance of wavelengths
involved in the regression equations (Martin et al., 2008; Smith et al., 2002; Smith
et al., 2003). The methodology developed in this chapter to estimate leaf
chemistry would be beneficial to ecologists, in particular those who are involved
130
with spectral and chemical analysis of tropical forests because it is less affected
by variations in species composition.
Chapter 4 employs a simulated spectral database to provide an evaluation
of the methodology developed in Chapter 3 to determine effective predictors of
leaf GWC. The PROSPECT radiative transfer model is able to accurately
represent the measured reflectance in the 800-2500 nm range, with M E’s less
than 0.03. Three of the six wavelet features derived from the simulated spectra are
in accordance with those derived from the measured spectra. The predictive
capability of these consistent wavelet features demonstrates that more spectral
information associated with leaf GWC could be extracted from the absorption
features of dry matter than from those of water. It is the decline in the strength of
water absorptions that makes the dry matter absorption more detectable in leaf
reflectance spectra (Kokaly & Clark; Tian et al., 2001). The wavelet-based
methodology, developed using measured spectra and tested using simulated
spectra, proves to be effective in predicting leaf GWC from reflectance spectra
even in the presence of a diverse set of tree species.
5.3. Avenues of future research
This thesis has investigated the detection of beetle attack stress and the
quantification of leaf water content using spectroscopic measurements at the leaf
level. Future research seeks to extend these studies to canopy level using airborne
or spaceborne hyperspectral imagery. Further research should either apply the
leaf-level wavelet features to hyperspectral imagery or revisit the problem using
canopy-level data. The methodologies presented in the thesis would first have to
be adapted to process imagery negatively impacted by atmospheric absorption.
For the spectral detection of green attack damage, a narrow feature region (1318-
1322 nm) was located on the edge of a strong atmospheric absorption region and
may still be of use dependent on the quality of the atmospheric correction for
hyperspectral imagery. High-frequency noise in imagery data is not a concern
since it could be readily removed with low-scale wavelets. As to the estimation of
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water content in vegetation canopies, there are also possibilities for
implementation on airborne data because multiple wavelet features have been
determined from across the shortwave infrared region (1300-2500 nm). However,
a question that arises is whether spectral properties at the leaf level could be
transferred to the canopy level due to the confounding effect of canopy
architecture and background materials within (Ahern, 1988; Daughtry et al., 2000;
Sánchez-Azofeifa & Castro-Esau, 2006). Fortunately, the reflectance signals from
water could be enhanced at the canopy level due to the more intensive multiple
scattering process within canopies (Asner, 1998; Sims & Gamon, 2003) and
background materials such as soil typically have little high frequency spectral
information.
Research opportunities also exist to apply the developed methodologies to
other data sets collected under different scenarios. The approach to detect green
attack damage could be evaluated using samples collected from other areas that
are also affected by the current outbreak of mountain pine beetle (e.g., British
Columbia). As to the estimation of leaf water content, the wavelet features
consistently derived in Chapter 3 and Chapter 4 are particularly useful for
ecosystems with considerable diversity in species composition, such as tropical
forests in Australia (Asner & Martin, 2008) and in Americas (Castro-Esau et al.,
2006; Sánchez-Azofeifa et al., 2009). Experience gained utilizing other data sets
will help to improve the procedure of feature selection on the correlation
scalogram. The number of features selected was dependent on the percentage
threshold that was set to an empirical value of 1% for all analyses. Further
exploration of the relationship between the threshold and the size and spatial
pattern of feature regions might suggest a better strategy to determine the
threshold. The distribution of a feature region as a function of wavelength and
scale also has implications for potential detection of representative features as
constrained by the resolution of airborne and spaceborne sensors. The pattern of
feature regions is also useful for refining feature selection in the future. As a
result of the feature selection procedure, the feature set may also be useful for
refining feature selection in the future.
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While constructing correlation scalograms, linear models were used to fit
the relationships between wavelet power and all dependent variables and these
models worked well as shown in Chapter 2. It was not appropriate to apply linear
fitting to LWCD in Chapter 3 but non-linear fitting could be avoided by
converting linearly modeled LWCF to LWCD. As this conversion is not generally
applicable, future work should investigate non-linear models such as polynomial
functions for the wavelet-based methodology to fit the relationship between
wavelet power and other leaf chemical constituents.
Although the wavelet features derived for the estimation of leaf GWC
were insensitive to species, the question of how to explicitly suppress the effect of
leaf structural variability on spectral reflectance using CWA remains. The
variation in leaf structural characteristics represented by the wide range of species
in the tropical data set could be quantified by a number of structural parameters
(Castro-Esau et al., 2006; Sánchez-Azofeifa et al., 2009). Future research could
focus on how to relate structural properties to spectral features in the wavelet
domain and then reducing the influences of those wavelet features on spectral
estimation of leaf water content. In addition, it is worth investigating whether it is
feasible to separate the spectral variability caused by structural properties and
chemical properties by means of multiscale representation of CWA. This is
important for hyperspectral applications where the effect of leaf structural
variability on spectral reflectance is to be minimized (Danson et al., 1992; Sims &
Gamon, 2002).
Other than foliar water, the methodology developed using the tropical leaf
data set could also be applied to quantify other chemical constituents such as
chlorophyll, nitrogen, lignin, and cellulose to better understand their roles in
ecosystem processes and biogeochemical cycles (Kokaly et al., 2009; Schimel,
1995; Wessman et al., 1998). In fact, the correlation scalogram includes a whole
set of features characterized by wavelength and scale in the wavelet domain. Here
I used a tropical data set to label the features sensitive to leaf water content. The
next step could be to identify and label the features sensitive to all other leaf
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chemical constituents used in the literature. This scalogram with labeling of
wavelet features has the potential to provide improved estimation of leaf
chemistry and valuable knowledge about the control of individual constituents on
leaf spectral properties.
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5.4. References
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reflectance of lodgepole pine. International Journal of Remote Sensing, 9,
1451-1468.
Asner, G. P., & Martin, R. E. (2008). Spectral and chemical analysis of tropical
forests: Scaling from leaf to canopy levels. Remote Sensing of
Environment, 112, 3958-3970.
Blackburn, G. A., & Ferwerda, J. G. (2008). Retrieval of chlorophyll
concentration from leaf reflectance spectra using wavelet analysis. Remote
Sensing of Environment, 112, 1614-1632.
Bruce, L. M., Morgan, C., & Larsen, S. (2001). Automated detection of subpixel
hyperspectral targets with continuous and discrete wavelet transforms. IEEE
Transactions on Geoscience and Remote Sensing, 39, 2217-2226.
Castro-Esau K. L. nchez-Azofeifa, G. A., Rivard, B., Wright, S. J., &
Quesada, M. (2006). Variability in leaf optical properties of mesoamerican
trees and the potential for species classification. American Journal of Botany,
93, 517-530.
Danson, F. M., & Bowyer, P. (2004). Estimating live fuel moisture content from
remotely sensed reflectance. Remote Sensing of Environment, 92, 309-321.
Daughtry, C. S. T., Walthall, C. L., Kim, M. S., De Colstoun, E. B., & McMurtrey
III, J. E. (2000). Estimating corn leaf chlorophyll concentration from leaf and
canopy reflectance. Remote Sensing of Environment, 74, 229-239.
Ferwerda, J. G., & Jones, S. (2006). Continuous wavelet transformations for
hyperspectral feature detection. Proceedings of the 12th International
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Austria.
Koger, C. H., Bruce, L. M., Shaw, D. R., & Reddy, K. N. (2003). Wavelet
analysis of hyperspectral reflectance data for detecting pitted morningglory
(Ipomoea lacunosa) in soybean (Glycine max). Remote Sensing of
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Kokaly, R. F., Asner, G. P., Ollinger, S. V., Martin, M. E., & Wessman, C. A.
(2009). Characterizing canopy biochemistry from imaging spectroscopy and
its application to ecosystem studies. Remote Sensing of Environment, 113,
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Kokaly, R. F., & Clark, R. N. (1999). Spectroscopic determination of leaf
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Martin, M. E., Plourde, L. C., Ollinger, S. V., Smith, M. -L., & McNeil, B. E.
(2008). A generalizable method for remote sensing of canopy nitrogen across
a wide range of forest ecosystems. Remote Sensing of Environment, 112,
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Pu, R., & Gong, P. (2004). Wavelet transform applied to EO-1 hyperspectral data
for forest LAI and crown closure mapping. Remote Sensing of Environment,
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wavelets for the improved use of spectral libraries and hyperspectral data.
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Runesson, U. T. (1991). Considerations for early remote detection of mountain
pine beetle in green-foliaged lodgepole pine. PhD Dissertation. University of
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hyperspectral properties of a community of tropical dry forest lianas and
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Sánchez-Azofeifa, G. A., Castro, K., Wright, S. J., Gamon, J., Kalacska, M.,
Rivard, B., Schnitzer, S. A. & Feng, J. L. (2009). Differences in leaf traits,
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Schimel, D. S. (1995). Terrestrial biogeochemical cycles: Global estimates with
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Sims, D. A., & Gamon, J. A. (2002). Relationships between leaf pigment content
and spectral reflectance across a wide range of species, leaf structures and
developmental stages. Remote Sensing of Environment, 81, 337-354.
Sims, D. A., & Gamon, J. A. (2003). Estimation of vegetation water content and
photosynthetic tissue area from spectral reflectance: A comparison of indices
based on liquid water and chlorophyll absorption features. Remote Sensing of
Environment, 84, 526-537.
Smith, M. -L., Martin, M. E., Plourde, L., & Ollinger, S. V. (2003). Analysis of
hyperspectral data for estimation of temperate forest canopy nitrogen
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41, 1332-1337.
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(2002). Direct estimation of aboveground forest productivity through hyperspectral
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Tian, Q., Tong, Q., Pu, R., Guo, X., & Zhao, C. (2001). Spectroscopic
determination of wheat water status using 1650-1850 nm spectral absorption
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APPENDIX
Appendix 1. Continuous wavelet transform of a reflectance spectrum
Fig. A-1. Schematic representation of the continuous wavelet transform
workflow.
Each reflectance spectrum in data sets used in this thesis is an input to the
continuous wavelet transform function implemented in a professional software
(IDL). The output for each input is a wavelet power scalogram showing wavelet
power (magnitude of a wavelet coefficient) as a function of wavelength and scale.
138
Two of the ten scale components are extracted from the wavelet power scalogram
and displayed at the bottom of Fig. A-1 as a Scale 3 spectrum and a Scale 7
spectrum. Both can be compared to the reflectance spectrum. The Scale 3
spectrum captures various absorption features and the Scale 7 spectrum captures
the overall shape of the reflectance spectrum.
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Appendix 2. Workflow of the wavelet-based methodology
Fig. A-2. Workflow of the wavelet-based methodology.
The general procedures of the wavelet-based methodology developed in
this thesis are the same for stress detection and water content estimation:
1. CWT is applied to each reflectance spectrum to calculate the wavelet
power as a function of wavelength and scale as displayed in Fig. A-1.
Each reflectance spectrum is transformed to a wavelet power
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scalogram and the outcome of this step is a series of wavelet power
scalograms for the samples in a data set (Fig. A-2A).
2. A correlation scalogram (Fig. A-2B) was constructed by establishing
the Pearson’s linear correlations between each element of the wavelet
power scalograms and a dependent variable (i.e., chlorophyll
concentration, water content, or class ID) across all samples. The
correlation scalogram reports a squared correlation coefficient (R2),
ranging in magnitude from 0 to 1, at each wavelength and scale. Each
element of the correlation scalogram represents a feature that could be
selected.
3. The features where R2 is not statistically significant (p>=0.05) are
masked. The remaining features are then sorted in descending order of
R2, and a threshold R
2 value is applied to delineate the top 1% features
that most strongly correlate with the dependent variable. These
features delineated by the threshold form a number of scattered feature
regions on the correlation scalogram (Fig. A-2C).
If the user is satisfied with the feature regions, the methodology terminates
here. Otherwise, an additional step is required to select the most representative
feature for each feature region because each region may carry redundant spectral
information across consecutive wavelengths and scales. This can be done by
determining a feature with the maximum R2 within each region and the feature is
expressed as (wavelength in nm, scale). Under this circumstance, the ultimate
output of the wavelet-based methodology is a small number of wavelet features
sparsely distributed on the correlation scalogram.
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